1
|
Salvia R, Mehboudi M, Perarnau-Llobet M. Critical Quantum Metrology Assisted by Real-Time Feedback Control. PHYSICAL REVIEW LETTERS 2023; 130:240803. [PMID: 37390423 DOI: 10.1103/physrevlett.130.240803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 03/27/2023] [Accepted: 05/30/2023] [Indexed: 07/02/2023]
Abstract
We investigate critical quantum metrology, that is, the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any nonadaptive strategy will fail to exploit quantum critical enhancement (i.e., precision beyond the shot-noise limit) for a sufficiently large number of particles N whenever our prior knowledge is limited. We then consider different adaptive strategies that can overcome this no-go result and illustrate their performance in the estimation of (i) a magnetic field using a probe of 1D spin Ising chain and (ii) the coupling strength in a Bose-Hubbard square lattice. Our results show that adaptive strategies with real-time feedback control can achieve sub-shot-noise scaling even with few measurements and substantial prior uncertainty.
Collapse
Affiliation(s)
- Raffaele Salvia
- Scuola Normale Superiore, I-56127 Pisa, Italy
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Mohammad Mehboudi
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | | |
Collapse
|
2
|
Pessoa P. Information geometry and Bose-Einstein condensation. CHAOS (WOODBURY, N.Y.) 2023; 33:033101. [PMID: 37003840 DOI: 10.1063/5.0136244] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 02/03/2023] [Indexed: 06/19/2023]
Abstract
It is a long held conjecture in the connection between information geometry (IG) and thermodynamics that the curvature endowed by IG diverges at phase transitions. Recent work on the IG of Bose-Einstein (BE) gases challenged this conjecture by saying that in the limit of fugacity approaching unit-where BE condensation is expected-the curvature does not diverge; rather, it converges to zero. However, as the discontinuous behavior that identifies condensation is only observed at the thermodynamic limit, a study of the IG curvature at a finite number of particles, N, is in order from which the thermodynamic behavior can be observed by taking the thermodynamic limit ( N→∞) posteriorly. This article presents such a study. We find that for a trapped gas, as N increases, the values of curvature decrease proportionally to a power of N, while the temperature at which the maximum value of curvature occurs approaches the usually defined critical temperature. This means that, in the thermodynamic limit, the curvature has a limited value where a phase transition is observed, contradicting the forementioned conjecture.
Collapse
Affiliation(s)
- Pedro Pessoa
- Physics Department, University at Albany (SUNY), Albany, New York 12222, USA
| |
Collapse
|
3
|
Kudler-Flam J. Rényi Mutual Information in Quantum Field Theory. PHYSICAL REVIEW LETTERS 2023; 130:021603. [PMID: 36706421 DOI: 10.1103/physrevlett.130.021603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Accepted: 12/23/2022] [Indexed: 06/18/2023]
Abstract
We study a proper definition of Rényi mutual information (RMI) in quantum field theory as defined via the Petz Rényi relative entropy. Unlike the standard definition, the RMI we compute is a genuine measure of correlations between subsystems, as evidenced by its non-negativity and monotonicity under local operations. Furthermore, the RMI is UV finite and well defined in the continuum limit. We develop a replica path integral approach for the RMI in quantum field theories and evaluate it explicitly in 1+1D conformal field theory using twist fields. We prove that it bounds connected correlation functions and check our results against exact numerics in the massless free fermion theory.
Collapse
Affiliation(s)
- Jonah Kudler-Flam
- School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA and Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
4
|
Wald S, Moreira SV, Semião FL. In- and out-of-equilibrium quantum metrology with mean-field quantum criticality. Phys Rev E 2020; 101:052107. [PMID: 32575218 DOI: 10.1103/physreve.101.052107] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Accepted: 04/15/2020] [Indexed: 06/11/2023]
Abstract
We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level. First, we focus on equilibrium quantum criticality in the SQS and obtain the quantum Fisher information analytically, which is associated with the minimum lower bound for the precision of estimation of the parameter driving the phase transition. We compare it with the Fisher information for a specific experimental scenario where photon-counting-like measurements are employed. We find how quantum criticality and squeezing are useful resources in the metrological scenario. Second, we obtain the quantum Fisher information for the out-of-equilibrium transition in the dissipative nonequilibrium steady state and investigate how the presence of dissipation affects the parameter estimation. In this scenario, it is known that the critical point is shifted by an amount which depends on the dissipation rate. This is used here to design high precision protocols for a whole range of the transition-driving parameter in the ordered phase. In fact, for certain values of the parameter being estimated, dissipation may be used to obtain higher precision when compared to the equilibrium scenario.
Collapse
Affiliation(s)
- Sascha Wald
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany
| | - Saulo V Moreira
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC-UFABC, Santo André, Brazil
| | - Fernando L Semião
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC-UFABC, Santo André, Brazil
| |
Collapse
|
5
|
Carollo A, Spagnolo B, Valenti D. Uhlmann curvature in dissipative phase transitions. Sci Rep 2018; 8:9852. [PMID: 29959332 PMCID: PMC6026214 DOI: 10.1038/s41598-018-27362-9] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Accepted: 05/10/2018] [Indexed: 11/09/2022] Open
Abstract
A novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions. NESS-QPTs offer a unique arena where such a distinction fades off. We propose a method to reveal and quantitatively assess the quantum character of such critical phenomena. We apply this tool to a paradigmatic class of lattice fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the Uhlmann curvature, the divergence of the correlation length, the character of the criticality and the dissipative gap are demonstrated. We argue that this tool can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.
Collapse
Affiliation(s)
- Angelo Carollo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy. .,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.
| | - Bernardo Spagnolo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123, Catania, Italy
| | - Davide Valenti
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Istituto di Biomedicina ed Immunologia Molecolare (IBIM) "Alberto Monroy", CNR, Via Ugo La Malfa 153, I-90146, Palermo, Italy
| |
Collapse
|
6
|
Symmetric Logarithmic Derivative of Fermionic Gaussian States. ENTROPY 2018; 20:e20070485. [PMID: 33265575 PMCID: PMC7513002 DOI: 10.3390/e20070485] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 06/16/2018] [Accepted: 06/16/2018] [Indexed: 01/24/2023]
Abstract
In this article, we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.
Collapse
|
7
|
Bina M, Amelio I, Paris MGA. Dicke coupling by feasible local measurements at the superradiant quantum phase transition. Phys Rev E 2016; 93:052118. [PMID: 27300841 DOI: 10.1103/physreve.93.052118] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Indexed: 06/06/2023]
Abstract
We address characterization of many-body superradiant systems and establish a fundamental connection between quantum criticality and the possibility of locally estimating the coupling constant, i.e., extracting its value by probing only a portion of the whole system. In particular, we consider Dicke-like superradiant systems made of an ensemble of two-level atoms interacting with a single-mode radiation field at zero effective temperature, and address estimation of the coupling by measurements performed only on radiation. At first, we obtain analytically the quantum Fisher information (QFI) and show that optimal estimation of the coupling may be achieved by tuning the frequency of the radiation field to drive the system toward criticality. The scaling behavior of the QFI at the critical point is obtained explicitly upon exploiting the symplectic formalism for Gaussian states. We then analyze the performances of feasible detection schemes performed only on the radiation subsystem, namely homodyne detection and photon counting, and show that the corresponding Fisher informations (FIs) approach the global QFI in the critical region. We thus conclude that criticality is a twofold resource. On the one hand, global QFI diverges at the critical point, i.e., the coupling may be estimated with the arbitrary precision. On the other hand, the FIs of feasible local measurements (which are generally smaller than the QFI out of the critical region), show the same scaling of the global QFI; i.e., optimal estimation of coupling may be achieved by locally probing the system, despite its strongly interacting nature.
Collapse
Affiliation(s)
- M Bina
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano, Italy
| | - I Amelio
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano, Italy
| | - M G A Paris
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano, Italy; CNISM, UdR Milano Statale, I-20133 Milano, Italy; and INFN, Sezione di Milano, I-20133 Milano, Italy
| |
Collapse
|
8
|
Banchi L, Braunstein SL, Pirandola S. Quantum Fidelity for Arbitrary Gaussian States. PHYSICAL REVIEW LETTERS 2015; 115:260501. [PMID: 26764978 DOI: 10.1103/physrevlett.115.260501] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Indexed: 05/26/2023]
Abstract
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Collapse
Affiliation(s)
- Leonardo Banchi
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Samuel L Braunstein
- Computer Science and York Centre for Quantum Technologies, University of York, York YO10 5GH, United Kingdom
| | - Stefano Pirandola
- Computer Science and York Centre for Quantum Technologies, University of York, York YO10 5GH, United Kingdom
| |
Collapse
|
9
|
Žnidarič M. Relaxation times of dissipative many-body quantum systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042143. [PMID: 26565204 DOI: 10.1103/physreve.92.042143] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Indexed: 06/05/2023]
Abstract
We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap cannot be larger than ∼1/L. In integrable systems with boundary dissipation one typically observes scaling of ∼1/L(3), while in chaotic ones one can have faster relaxation with the gap scaling as ∼1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.
Collapse
Affiliation(s)
- Marko Žnidarič
- Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
| |
Collapse
|
10
|
Zanardi P, Campos Venuti L. Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems. PHYSICAL REVIEW LETTERS 2014; 113:240406. [PMID: 25541757 DOI: 10.1103/physrevlett.113.240406] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2014] [Indexed: 06/04/2023]
Abstract
Recently, it has been realized that dissipative processes can be harnessed and exploited to the end of coherent quantum control and information processing. In this spirit, we consider strongly dissipative quantum systems admitting a nontrivial manifold of steady states. We show how one can enact adiabatic coherent unitary manipulations, e.g., quantum logical gates, inside this steady-state manifold by adding a weak, time-rescaled, Hamiltonian term into the system's Liouvillian. The effective long-time dynamics is governed by a projected Hamiltonian which results from the interplay between the weak unitary control and the fast relaxation process. The leakage outside the steady-state manifold entailed by the Hamiltonian term is suppressed by an environment-induced symmetrization of the dynamics. We present applications to quantum-computation in decoherence-free subspaces and noiseless subsystems and numerical analysis of nonadiabatic errors.
Collapse
Affiliation(s)
- Paolo Zanardi
- Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA
| | - Lorenzo Campos Venuti
- Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA
| |
Collapse
|