1
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Majidy S. Noncommuting charges can remove non-stationary quantum many-body dynamics. Nat Commun 2024; 15:8246. [PMID: 39304665 DOI: 10.1038/s41467-024-52588-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Accepted: 09/11/2024] [Indexed: 09/22/2024] Open
Abstract
Studying noncommuting conserved quantities, or 'charges,' has revealed a conceptual puzzle: noncommuting charges hinder thermalization in some ways yet promote it in others. While many quantum systems thermalize according to the Eigenstate Thermalization Hypothesis (ETH), systems with 'dynamical symmetries' violate the ETH and exhibit non-stationary dynamics, preventing them from equilibrating, much less thermalizing. We demonstrate that each pair of dynamical symmetries corresponds to a specific charge. We find that introducing new charges that do not commute with existing ones disrupts these symmetries, thereby eliminating non-stationary dynamics and facilitating thermalization. We illustrate this behavior across various models, including the Hubbard model and Heisenberg spin chains. Our findings demonstrate that noncommuting charges can enhance thermalization by reducing the number of local observables that thermalize according to the ETH.
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Affiliation(s)
- Shayan Majidy
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada.
- Department of Physics, Harvard University, Cambridge, MA, USA.
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2
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García-Pintos LP, Bharti K, Bringewatt J, Dehghani H, Ehrenberg A, Yunger Halpern N, Gorshkov AV. Estimation of Hamiltonian Parameters from Thermal States. PHYSICAL REVIEW LETTERS 2024; 133:040802. [PMID: 39121410 DOI: 10.1103/physrevlett.133.040802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Accepted: 06/10/2024] [Indexed: 08/11/2024]
Abstract
We upper bound and lower bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/sqrt[n], beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g., a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.
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Affiliation(s)
| | - Kishor Bharti
- Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- A*STAR Quantum Innovation Centre (Q.InC), Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, # 16-16 Connexis, Singapore 138632, Republic of Singapore
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3
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Marvian I, Liu H, Hulse A. Rotationally Invariant Circuits: Universality with the Exchange Interaction and Two Ancilla Qubits. PHYSICAL REVIEW LETTERS 2024; 132:130201. [PMID: 38613310 DOI: 10.1103/physrevlett.132.130201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2022] [Revised: 12/14/2023] [Accepted: 02/13/2024] [Indexed: 04/14/2024]
Abstract
Universality of local unitary transformations is one of the cornerstones of quantum computing with many applications and implications that go beyond this field. However, it has recently been shown that this universality does not hold in the presence of continuous symmetries: generic symmetric unitaries on a composite system cannot be implemented, even approximately, using local symmetric unitaries on the subsystems. In this Letter, we show that, despite these constraints, any SU(2) rotationally invariant unitary can be realized with the Heisenberg exchange interaction, which is 2-local and rotationally invariant, provided that the system interacts with a pair of ancilla qubits. We also show that a single ancilla is not enough to achieve universality. Furthermore, we study qubit circuits formed from k-local rotationally invariant unitaries and fully characterize the constraints imposed by locality on the realizable unitaries. We also find an interpretation of these constraints in terms of the average energy of states with a fixed angular momentum.
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Affiliation(s)
- Iman Marvian
- Departments of Physics, Duke University, Durham, North Carolina 27708, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
- Duke Quantum Center, Durham, North Carolina 27708, USA
| | - Hanqing Liu
- Departments of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Austin Hulse
- Departments of Physics, Duke University, Durham, North Carolina 27708, USA
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4
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Pei JH, Chen JF, Quan HT. Exploring quasiprobability approaches to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution. Phys Rev E 2023; 108:054109. [PMID: 38115414 DOI: 10.1103/physreve.108.054109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 10/09/2023] [Indexed: 12/21/2023]
Abstract
In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general way to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit.
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Affiliation(s)
- Ji-Hui Pei
- School of Physics, Peking University, Beijing 100871, China
| | - Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
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5
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Somhorst FHB, van der Meer R, Correa Anguita M, Schadow R, Snijders HJ, de Goede M, Kassenberg B, Venderbosch P, Taballione C, Epping JP, van den Vlekkert HH, Timmerhuis J, Bulmer JFF, Lugani J, Walmsley IA, Pinkse PWH, Eisert J, Walk N, Renema JJ. Quantum simulation of thermodynamics in an integrated quantum photonic processor. Nat Commun 2023; 14:3895. [PMID: 37393275 DOI: 10.1038/s41467-023-38413-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2022] [Accepted: 05/02/2023] [Indexed: 07/03/2023] Open
Abstract
One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is neither. The resolution to this paradox is to recognize that global unitary evolution of a multi-partite quantum state causes the state of local subsystems to evolve towards maximum-entropy states. In this work, we experimentally demonstrate this effect in linear quantum optics by simultaneously showing the convergence of local quantum states to a generalized Gibbs ensemble constituting a maximum-entropy state under precisely controlled conditions, while introducing an efficient certification method to demonstrate that the state retains global purity. Our quantum states are manipulated by a programmable integrated quantum photonic processor, which simulates arbitrary non-interacting Hamiltonians, demonstrating the universality of this phenomenon. Our results show the potential of photonic devices for quantum simulations involving non-Gaussian states.
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Affiliation(s)
- F H B Somhorst
- MESA+ Institute for Nanotechnology, University of Twente, P. O. box 217, 7500 AE, Enschede, The Netherlands
| | - R van der Meer
- MESA+ Institute for Nanotechnology, University of Twente, P. O. box 217, 7500 AE, Enschede, The Netherlands
| | - M Correa Anguita
- MESA+ Institute for Nanotechnology, University of Twente, P. O. box 217, 7500 AE, Enschede, The Netherlands
| | - R Schadow
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany
| | - H J Snijders
- QuiX Quantum B.V., Hengelosestraat 500, 7521 AN, Enschede, The Netherlands
| | - M de Goede
- QuiX Quantum B.V., Hengelosestraat 500, 7521 AN, Enschede, The Netherlands
| | - B Kassenberg
- QuiX Quantum B.V., Hengelosestraat 500, 7521 AN, Enschede, The Netherlands
| | - P Venderbosch
- QuiX Quantum B.V., Hengelosestraat 500, 7521 AN, Enschede, The Netherlands
| | - C Taballione
- QuiX Quantum B.V., Hengelosestraat 500, 7521 AN, Enschede, The Netherlands
| | - J P Epping
- QuiX Quantum B.V., Hengelosestraat 500, 7521 AN, Enschede, The Netherlands
| | | | - J Timmerhuis
- MESA+ Institute for Nanotechnology, University of Twente, P. O. box 217, 7500 AE, Enschede, The Netherlands
| | - J F F Bulmer
- Quantum Engineering Technology Labs, University of Bristol, Bristol, UK
| | - J Lugani
- Center for Sensors, Instrumentation and Cyber Physical System Engineering, IIT Delhi, New Delhi, 110 016, India
| | - I A Walmsley
- Department of Physics, Imperial College London, Prince Consort Rd., London, SW7 2AZ, UK
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
| | - P W H Pinkse
- MESA+ Institute for Nanotechnology, University of Twente, P. O. box 217, 7500 AE, Enschede, The Netherlands
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany.
- Helmholtz-Zentrum Berlin für Materialien und Energie, 14109, Berlin, Germany.
- Fraunhofer Heinrich Hertz Institute, 10587, Berlin, Germany.
| | - N Walk
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany.
| | - J J Renema
- MESA+ Institute for Nanotechnology, University of Twente, P. O. box 217, 7500 AE, Enschede, The Netherlands.
- QuiX Quantum B.V., Hengelosestraat 500, 7521 AN, Enschede, The Netherlands.
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6
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Murthy C, Babakhani A, Iniguez F, Srednicki M, Yunger Halpern N. Non-Abelian Eigenstate Thermalization Hypothesis. PHYSICAL REVIEW LETTERS 2023; 130:140402. [PMID: 37084457 DOI: 10.1103/physrevlett.130.140402] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Revised: 10/16/2022] [Accepted: 02/24/2023] [Indexed: 05/03/2023]
Abstract
The eigenstate thermalization hypothesis (ETH) explains why nonintegrable quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector-in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local operators' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.
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Affiliation(s)
- Chaitanya Murthy
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Arman Babakhani
- Department of Physics, University of Southern California, Los Angeles, California 90089, USA
- Information Sciences Institute, Marina Del Rey, California 90292, USA
| | - Fernando Iniguez
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Mark Srednicki
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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7
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Corps ÁL, Relaño A. Theory of Dynamical Phase Transitions in Quantum Systems with Symmetry-Breaking Eigenstates. PHYSICAL REVIEW LETTERS 2023; 130:100402. [PMID: 36962016 DOI: 10.1103/physrevlett.130.100402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 10/03/2022] [Accepted: 02/16/2023] [Indexed: 06/18/2023]
Abstract
We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite-range interactions, both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a nonzero value of the dynamical order parameter characterizing DPTs-I, and precludes the main mechanism giving rise to nonanalyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the incompatibility of the main mechanism for DPTs-II with the presence of this additional conserved charge. Our results are numerically illustrated in the fully connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions. Finally, we discuss the applicability of our theory to systems with finite-range interactions, where the phenomenology of excited-state quantum phase transitions is absent. We illustrate our findings by means of numerical calculations with experimentally relevant initial states.
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Affiliation(s)
- Ángel L Corps
- Instituto de Estructura de la Materia, IEM-CSIC, Serrano 123, E-28006 Madrid, Spain
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
| | - Armando Relaño
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid, Avenida Complutense s/n, E-28040 Madrid, Spain
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8
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Noh JD. Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry. Phys Rev E 2023; 107:014130. [PMID: 36797888 DOI: 10.1103/physreve.107.014130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
We investigate the eigenstate thermalization properties of the spin-1/2 XXZ model in two-dimensional rectangular lattices of size L_{1}×L_{2} under periodic boundary conditions. Exploiting the symmetry property, we can perform an exact diagonalization study of the energy eigenvalues up to system size 4×7 and of the energy eigenstates up to 4×6. Numerical analysis of the Hamiltonian eigenvalue spectrum and matrix elements of an observable in the Hamiltonian eigenstate basis supports that the two-dimensional XXZ model follows the eigenstate thermalization hypothesis. When the spin interaction is isotropic, the XXZ model Hamiltonian conserves the total spin and has SU(2) symmetry. We show that the eigenstate thermalization hypothesis is still valid within each subspace where the total spin is a good quantum number.
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Affiliation(s)
- Jae Dong Noh
- Department of Physics, University of Seoul, Seoul 02504, Korea
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9
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Banerjee A, Kibe T, Mittal N, Mukhopadhyay A, Roy P. Erasure Tolerant Quantum Memory and the Quantum Null Energy Condition in Holographic Systems. PHYSICAL REVIEW LETTERS 2022; 129:191601. [PMID: 36399741 DOI: 10.1103/physrevlett.129.191601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 06/11/2022] [Accepted: 10/19/2022] [Indexed: 06/16/2023]
Abstract
Investigating principles for storage of quantum information at finite temperature with minimal need for active error correction is an active area of research. We bear upon this question in two-dimensional holographic conformal field theories via the quantum null energy condition that we have shown earlier to implement the restrictions imposed by quantum thermodynamics on such many-body systems. We study an explicit encoding of a logical qubit into two similar chirally propagating excitations of finite von Neumann entropy on a finite temperature background whose erasure can be implemented by an appropriate inhomogeneous and instantaneous energy-momentum inflow from an infinite energy memoryless bath due to which the system transits to a thermal state. Holographically, these fast erasure processes can be depicted by generalized AdS-Vaidya geometries described previously in which no assumption of specific form of bulk matter is needed. We show that the quantum null energy condition gives analytic results for the minimal finite temperature needed for the deletion which is larger than the initial background temperature in consistency with Landauer's principle. In particular, we find a simple expression for the minimum final temperature needed for the erasure of a large number of encoding qubits. We also find that if the encoding qubits are localized over an interval shorter than a specific localization length, then the fast erasure process is impossible, and furthermore this localization length is the largest for an optimal amount of encoding qubits determined by the central charge. We estimate the optimal encoding qubits for realistic protection against fast erasure. We discuss possible generalizations of our study for novel constructions of fault-tolerant quantum gates operating at finite temperature.
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Affiliation(s)
- Avik Banerjee
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Tanay Kibe
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Nehal Mittal
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Ayan Mukhopadhyay
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Pratik Roy
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
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10
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Cerisola F, Sapienza F, Roncaglia AJ. Heat engines with single-shot deterministic work extraction. Phys Rev E 2022; 106:034135. [PMID: 36266866 DOI: 10.1103/physreve.106.034135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 08/16/2022] [Indexed: 06/16/2023]
Abstract
We introduce heat engines working in the nanoregime that allow one to extract a finite amount of deterministic work. Using the resource theory approach to themodynamics, we show that the efficiency of these cycles is strictly smaller than Carnot's, and we associate this difference with a fundamental irreversibility that is present in single-shot transformations. When fluctuations in the extracted work are allowed there is a trade-off between their size and the efficiency. As the size of fluctuations increases so does the efficiency and optimal efficiency is attained for unbounded fluctuations, while a certain amount of deterministic work is drawn from the cycle. Finally, we show that when the working medium is composed of many particles, by creating an amount of correlations between the subsystems that scale logarithmically with their number, Carnot's efficiency can also be approached in the asymptotic limit along with deterministic work extraction.
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Affiliation(s)
- Federico Cerisola
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
- Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
| | - Facundo Sapienza
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- Department of Statistics, University of California, Berkeley, 367 Evans Hall, Berkeley, California 94720, USA
| | - Augusto J Roncaglia
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
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11
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Kibe T, Mukhopadhyay A, Roy P. Quantum Thermodynamics of Holographic Quenches and Bounds on the Growth of Entanglement from the Quantum Null Energy Condition. PHYSICAL REVIEW LETTERS 2022; 128:191602. [PMID: 35622045 DOI: 10.1103/physrevlett.128.191602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Revised: 03/20/2022] [Accepted: 04/21/2022] [Indexed: 06/15/2023]
Abstract
The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a subregion along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, is necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentums that are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the nonsaturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length l always thermalizes in time l/2 with an exponent 3/2. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any l, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.
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Affiliation(s)
- Tanay Kibe
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Ayan Mukhopadhyay
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Pratik Roy
- Center for Quantum Information Theory of Matter and Spacetime, and Center for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
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12
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Haldar A, Das A. Statistical mechanics of Floquet quantum matter: exact and emergent conservation laws. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:234001. [PMID: 34020440 DOI: 10.1088/1361-648x/ac03d2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 05/21/2021] [Indexed: 06/12/2023]
Abstract
Equilibrium statistical mechanics rests on the assumption of chaotic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant conservation laws in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics of Floquet systems has a much richer structure due to the existence ofemergentconservation laws: these are approximate but stable conservation laws arisingdue to the drive, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This indicates to the possibility of stable Floquet phases of matter in disorder-free systems. This review intends to give a self-contained theoretical overview of these developments for a broad physics audience. We conclude by briefly surveying the current experimental scenario.
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Affiliation(s)
- Asmi Haldar
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnab Das
- Indian Association for the Cultivation of Science (School of Physical Sciences), 2A & 2B Raja S. C. Mullick Road, Kolkata 700032, India
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13
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Currencies in Resource Theories. ENTROPY 2021; 23:e23060755. [PMID: 34204010 PMCID: PMC8233888 DOI: 10.3390/e23060755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Revised: 06/09/2021] [Accepted: 06/11/2021] [Indexed: 11/24/2022]
Abstract
How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of “currencies” to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out. Currencies are a subset of resources chosen to quantify all the other resources—like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions in the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work generalizes axiomatic approaches to thermodynamic entropy, work and currencies made of local copies. In particular, by applying our approach to the resource theory of unital maps, we derive operational single-shot entropies for arbitrary, non-probabilistic descriptions of resources.
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14
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Alimuddin M, Guha T, Parashar P. Structure of passive states and its implication in charging quantum batteries. Phys Rev E 2020; 102:022106. [PMID: 32942516 DOI: 10.1103/physreve.102.022106] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Accepted: 07/10/2020] [Indexed: 11/07/2022]
Abstract
In this article, in addition to the characterization of geometrical state spaces for the passive states, an operational approach has been introduced to distinguish them on their charging capabilities of a quantum battery. Unlike the thermal states, the structural instability of passive states assures the existence of a natural number n, for which n+1 copies of the state can charge a quantum battery while n copies cannot. This phenomenon can be presented in an n copy resource-theoretic approach, for which the free states are unable to charge the battery in n copies. Here we have exhibited the single copy scenario explicitly. We also show that general ordering of the passive states on the basis of their charging capabilities is not possible and even the macroscopic entities (viz. energy and entropy) are unable to order them precisely. Interestingly, for some of the passive states, the majorization criterion gives sufficient order to the charging and discharging capabilities. However, the charging capacity for the set of thermal states (for which charging is possible) is directly proportional to their temperature.
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Affiliation(s)
- Mir Alimuddin
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Tamal Guha
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
| | - Preeti Parashar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata-700108, India
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15
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Popescu S, Sainz AB, Short AJ, Winter A. Reference Frames Which Separately Store Noncommuting Conserved Quantities. PHYSICAL REVIEW LETTERS 2020; 125:090601. [PMID: 32915626 DOI: 10.1103/physrevlett.125.090601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2019] [Revised: 04/27/2020] [Accepted: 07/28/2020] [Indexed: 06/11/2023]
Abstract
Even in the presence of conservation laws, one can perform arbitrary transformations on a system if given access to a suitable reference frame, since conserved quantities may be exchanged between the system and the frame. Here we explore whether these quantities can be separated into different parts of the reference frame, with each part acting as a "battery" for a distinct quantity. For systems composed of spin-1/2 particles, we show that the components of angular momentum S_{x}, S_{y}, and S_{z} (noncommuting conserved quantities) may be separated in this way, and also provide several extensions of this result. These results also play a key role in the quantum thermodynamics of noncommuting conserved quantities.
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Affiliation(s)
- Sandu Popescu
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Ana Belén Sainz
- International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland
- Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5 Ontario, Canada
| | - Anthony J Short
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Andreas Winter
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, 08010 Barcelona, Spain
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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16
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Yunger Halpern N, Beverland ME, Kalev A. Noncommuting conserved charges in quantum many-body thermalization. Phys Rev E 2020; 101:042117. [PMID: 32422760 DOI: 10.1103/physreve.101.042117] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2019] [Accepted: 03/17/2020] [Indexed: 11/07/2022]
Abstract
In statistical mechanics, a small system exchanges conserved quantities-heat, particles, electric charge, etc.-with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
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Affiliation(s)
- Nicole Yunger Halpern
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.,ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA.,Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | | | - Amir Kalev
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742-2420, USA
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17
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Beretta GP. The fourth law of thermodynamics: steepest entropy ascent. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190168. [PMID: 32223406 DOI: 10.1098/rsta.2019.0168] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/18/2019] [Indexed: 05/18/2023]
Abstract
When thermodynamics is understood as the science (or art) of constructing effective models of natural phenomena by choosing a minimal level of description capable of capturing the essential features of the physical reality of interest, the scientific community has identified a set of general rules that the model must incorporate if it aspires to be consistent with the body of known experimental evidence. Some of these rules are believed to be so general that we think of them as laws of Nature, such as the great conservation principles, whose 'greatness' derives from their generality, as masterfully explained by Feynman in one of his legendary lectures. The second law of thermodynamics is universally contemplated among the great laws of Nature. In this paper, we show that in the past four decades, an enormous body of scientific research devoted to modelling the essential features of non-equilibrium natural phenomena has converged from many different directions and frameworks towards the general recognition (albeit still expressed in different but equivalent forms and language) that another rule is also indispensable and reveals another great law of Nature that we propose to call the 'fourth law of thermodynamics'. We state it as follows: every non-equilibrium state of a system or local subsystem for which entropy is well defined must be equipped with a metric in state space with respect to which the irreversible component of its time evolution is in the direction of steepest entropy ascent compatible with the conservation constraints. To illustrate the power of the fourth law, we derive (nonlinear) extensions of Onsager reciprocity and fluctuation-dissipation relations to the far-non-equilibrium realm within the framework of the rate-controlled constrained-equilibrium approximation (also known as the quasi-equilibrium approximation). This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.
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18
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Faist P, Sagawa T, Kato K, Nagaoka H, Brandão FGSL. Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2019; 123:250601. [PMID: 31922799 DOI: 10.1103/physrevlett.123.250601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2019] [Indexed: 06/10/2023]
Abstract
The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the gap between the min- and the max-relative entropies to the thermal state is small, then the state can be approximately reversibly converted to and from the thermal state with thermal operations and a small source of coherence. Our proof provides a quantum version of the Shannon-McMillan-Breiman theorem for the relative entropy and a quantum Stein's lemma for ergodic states and local Gibbs states. Our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.
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Affiliation(s)
- Philippe Faist
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Institute for Theoretical Physics, ETH Zurich 8093, Switzerland
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
| | - Kohtaro Kato
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Hiroshi Nagaoka
- The University of Electro-Communications, Tokyo 182-8585, Japan
| | - Fernando G S L Brandão
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Google Inc., Venice, California 90291, USA
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19
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Lostaglio M. An introductory review of the resource theory approach to thermodynamics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:114001. [PMID: 31546240 DOI: 10.1088/1361-6633/ab46e5] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics covered include the so-called 'many second laws of thermodynamics', thermo-majorisation and symmetry constraints on the evolution of quantum coherence. Among the elementary applications, I explicitly work out the bounds on deterministic work extraction and formation, discuss the complete solution of the theory for a single qubit and present the irreversibility of coherence transfers. The aim is to facilitate the task of those researchers interested in engaging and contributing to this topic, presenting scope and motivation of its core assumptions and discussing the relation between the resource theory and complementary approaches.
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Affiliation(s)
- Matteo Lostaglio
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), 08860, Spain
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20
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Time-Energy and Time-Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations. ENTROPY 2019; 21:e21070679. [PMID: 33267393 PMCID: PMC7515176 DOI: 10.3390/e21070679] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Revised: 07/07/2019] [Accepted: 07/08/2019] [Indexed: 11/29/2022]
Abstract
In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam–Tamm–Messiah time–energy uncertainty relation τFΔH≥ℏ/2 provides a general lower bound to the characteristic time τF=ΔF/|d〈F〉/dt| with which the mean value of a generic quantum observable F can change with respect to the width ΔF of its uncertainty distribution (square root of F fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller energy uncertainty ΔH (square root of energy fluctuations). Here we show that when unitary evolution is complemented with a steepest-entropy-ascent model of dissipation, the resulting nonlinear master equation entails that these lower bounds get modified and depend also on the entropy uncertainty ΔS (square root of entropy fluctuations). For example, we obtain the time–energy-and–time–entropy uncertainty relation (2τFΔH/ℏ)2+(τFΔS/kBτ)2≥1 where τ is a characteristic dissipation time functional that for each given state defines the strength of the nonunitary, steepest-entropy-ascent part of the assumed master equation. For purely dissipative dynamics this reduces to the time–entropy uncertainty relation τFΔS≥kBτ, meaning that the nonequilibrium dissipative states with longer lifetime are those with smaller entropy uncertainty ΔS.
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21
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Abstract
The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In this work, we study the role of correlations in the thermodynamic process of state formation in the single-shot regime, and find that correlations can also be viewed as a resource. First, we show that the energetic cost of creating multiple copies of a given state can be reduced by allowing correlations in the final state. We obtain the minimum cost for every finite number of subsystems, and then we show that this feature is not restricted to the case of copies. More generally, we demonstrate that in the asymptotic limit, by allowing a logarithmic amount of correlations, we can recover standard results where the free energy quantifies this minimum cost. Correlations in quantum thermodynamics are usually regarded as a useful but expensive resource. Here, the authors prove that the work cost of generating multiple copies of a state is lower if the copies are correlated, pointing out at the irreversibility of the process in the single-shot regime.
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22
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Faist P, Berta M, Brandão F. Thermodynamic Capacity of Quantum Processes. PHYSICAL REVIEW LETTERS 2019; 122:200601. [PMID: 31172741 DOI: 10.1103/physrevlett.122.200601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Revised: 03/18/2019] [Indexed: 06/09/2023]
Abstract
Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state-as for instance in the case of an ideal gas-the possible transformations become reversible and are fully characterized by the free energy. In this Letter, we present a thermodynamic resource theory for quantum processes that also becomes reversible in the macroscopic limit, a property that is especially rare for a resource theory of quantum channels. We identify a unique single-letter and additive quantity, the thermodynamic capacity, that characterizes the "thermodynamic value" of a quantum channel, in the sense that the work required to simulate many repetitions of a quantum process employing many repetitions of another quantum process becomes equal to the difference of the respective thermodynamic capacities. On a technical level, we provide asymptotically optimal constructions of universal implementations of quantum processes. A challenging aspect of this construction is the apparent necessity to coherently combine thermal engines that would run in different thermodynamic regimes depending on the input state. Our results have applications in quantum Shannon theory by providing a generalized notion of quantum typical subspaces and by giving an operational interpretation to the entropy difference of a channel.
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Affiliation(s)
- Philippe Faist
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
| | - Mario Berta
- Department of Computing, Imperial College London, London SW7 2AZ, United Kingdom
| | - Fernando Brandão
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
- Google Inc., Venice, California 90291, USA
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23
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Gour G, Jennings D, Buscemi F, Duan R, Marvian I. Quantum majorization and a complete set of entropic conditions for quantum thermodynamics. Nat Commun 2018; 9:5352. [PMID: 30559428 PMCID: PMC6297236 DOI: 10.1038/s41467-018-06261-7] [Citation(s) in RCA: 57] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Accepted: 08/20/2018] [Indexed: 11/09/2022] Open
Abstract
What does it mean for one quantum process to be more disordered than another? Interestingly, this apparently abstract question arises naturally in a wide range of areas such as information theory, thermodynamics, quantum reference frames, and the resource theory of asymmetry. Here we use a quantum-mechanical generalization of majorization to develop a framework for answering this question, in terms of single-shot entropies, or equivalently, in terms of semi-definite programs. We also investigate some of the applications of this framework, and remarkably find that, in the context of quantum thermodynamics it provides the first complete set of necessary and sufficient conditions for arbitrary quantum state transformations under thermodynamic processes, which rigorously accounts for quantum-mechanical properties, such as coherence. Our framework of generalized thermal processes extends thermal operations, and is based on natural physical principles, namely, energy conservation, the existence of equilibrium states, and the requirement that quantum coherence be accounted for thermodynamically.
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Affiliation(s)
- Gilad Gour
- Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4, Canada. .,Institute for Quantum Science and Technology, University of Calgary, Calgary, AB, T2N 1N4, Canada.
| | - David Jennings
- Department of Physics, University of Oxford, Oxford, OX1 3PU, UK.,Department of Physics, Imperial College London, London, SW7 2AZ, UK
| | - Francesco Buscemi
- Department of Mathematical Informatics, Nagoya University, Chikusa-ku, Nagoya, 464-8601, Japan
| | - Runyao Duan
- Institute for Quantum Computing, Baidu Inc., 100193, Beijing, China.,Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, 2007, Australia
| | - Iman Marvian
- Departments of Physics & Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA
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24
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Popescu S, Sainz AB, Short AJ, Winter A. Quantum reference frames and their applications to thermodynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2018.0111. [PMID: 29807906 PMCID: PMC5990656 DOI: 10.1098/rsta.2018.0111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/11/2018] [Indexed: 05/06/2023]
Abstract
We construct a quantum reference frame, which can be used to approximately implement arbitrary unitary transformations on a system in the presence of any number of extensive conserved quantities, by absorbing any back action provided by the conservation laws. Thus, the reference frame at the same time acts as a battery for the conserved quantities. Our construction features a physically intuitive, clear and implementation-friendly realization. Indeed, the reference system is composed of the same types of subsystems as the original system and is finite for any desired accuracy. In addition, the interaction with the reference frame can be broken down into two-body terms coupling the system to one of the reference frame subsystems at a time. We apply this construction to quantum thermodynamic set-ups with multiple, possibly non-commuting conserved quantities, which allows for the definition of explicit batteries in such cases.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
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Affiliation(s)
- Sandu Popescu
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK
| | - Ana Belén Sainz
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - Anthony J Short
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK
| | - Andreas Winter
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys 23, 08010 Barcelona, Spain
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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25
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Ma X, You C, Adhikari S, Matekole ES, Glasser RT, Lee H, Dowling JP. Sub-shot-noise-limited phase estimation via SU(1,1) interferometer with thermal states. OPTICS EXPRESS 2018; 26:18492-18504. [PMID: 30114028 DOI: 10.1364/oe.26.018492] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Accepted: 06/06/2018] [Indexed: 06/08/2023]
Abstract
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a thermal state and a squeezed vacuum state as inputs and parity detection as the measurement. We find that the phase sensitivity can beat the shot-noise limit and approaches the Heisenberg limit, with increasing input photon number, in an ideal situation. We also consider the effect of various noises, including photon loss, dark counts, and thermal photon noise. Our results show that the phase sensitivity is below the shot-noise limit with photon loss and dark counts, but cannot beat the shot-noise limit in the presence of thermal noise.
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26
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Revealing missing charges with generalised quantum fluctuation relations. Nat Commun 2018; 9:2006. [PMID: 29789555 PMCID: PMC5964258 DOI: 10.1038/s41467-018-04407-1] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 04/27/2018] [Indexed: 11/08/2022] Open
Abstract
The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or ‘charges’), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices. Conservation laws are a key ingredient in the non-equilibrium dynamics of quantum many-body systems. Here, the authors develop generalised quantum fluctuation relations in order to identify the presence of conserved quantities relevant for a generalised Gibbs ensemble.
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27
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Abstract
Maximum-entropy ensembles are key primitives in statistical mechanics. Several approaches have been developed in order to justify the use of these ensembles in statistical descriptions. However, there is still no full consensus on the precise reasoning justifying the use of such ensembles. In this work, we provide an approach to derive maximum-entropy ensembles, taking a strictly operational perspective. We investigate the set of possible transitions that a system can undergo together with an environment, when one only has partial information about the system and its environment. The set of these transitions encodes thermodynamic laws and limitations on thermodynamic tasks as particular cases. Our main result is that the possible transitions are exactly those that are possible if both system and environment are assigned the maximum-entropy state compatible with the partial information. This justifies the overwhelming success of such ensembles and provides a derivation independent of typicality or information-theoretic measures. The minimal amount of assumptions to justify the use of maximum-entropy ensembles is still debated. Here, the authors show that the transitions that a partially known system environment can undergo are the same allowed for the maximum entropy state which is compatible with the known information.
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28
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Ito K, Hayashi M. Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond independent-and-identical-distribution scaling. Phys Rev E 2018; 97:012129. [PMID: 29448373 DOI: 10.1103/physreve.97.012129] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Indexed: 06/08/2023]
Abstract
In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-independent-and-identical-distribution scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.
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Affiliation(s)
- Kosuke Ito
- Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
| | - Masahito Hayashi
- Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
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29
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Croucher T, Bedkihal S, Vaccaro JA. Discrete Fluctuations in Memory Erasure without Energy Cost. PHYSICAL REVIEW LETTERS 2017; 118:060602. [PMID: 28234546 DOI: 10.1103/physrevlett.118.060602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Indexed: 06/06/2023]
Abstract
According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with an intrinsically discrete degree of freedom. Here we study the discrete fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.
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Affiliation(s)
- Toshio Croucher
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Salil Bedkihal
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Joan A Vaccaro
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
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30
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Guryanova Y, Popescu S, Short AJ, Silva R, Skrzypczyk P. Thermodynamics of quantum systems with multiple conserved quantities. Nat Commun 2016; 7:12049. [PMID: 27384384 PMCID: PMC4941046 DOI: 10.1038/ncomms12049] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Accepted: 05/23/2016] [Indexed: 11/08/2022] Open
Abstract
Recently, there has been much progress in understanding the thermodynamics of quantum systems, even for small individual systems. Most of this work has focused on the standard case where energy is the only conserved quantity. Here we consider a generalization of this work to deal with multiple conserved quantities. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and stored in its own battery. Unlike the standard case, in which the amount of extractable energy is constrained, here there is no limit on how much of any individual conserved quantity can be extracted. However, other conserved quantities must be supplied, and the second law constrains the combination of extractable quantities and the trade-offs between them. We present explicit protocols that allow us to perform arbitrarily good trade-offs and extract arbitrarily good combinations of conserved quantities from individual quantum systems.
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Affiliation(s)
- Yelena Guryanova
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - Sandu Popescu
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - Anthony J. Short
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - Ralph Silva
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
- Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland
| | - Paul Skrzypczyk
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
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