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Molitor OAD, Rudnicki Ł. Quantum Switch as a Thermodynamic Resource in the Context of Passive States. Entropy (Basel) 2024; 26:153. [PMID: 38392408 PMCID: PMC10888383 DOI: 10.3390/e26020153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Revised: 02/03/2024] [Accepted: 02/07/2024] [Indexed: 02/24/2024]
Abstract
In recent years, many works have explored possible advantages of indefinite causal order, with the main focus on its controlled implementation known as quantum switch. In this paper, we tackle advantages in quantum thermodynamics, studying whether quantum switch is capable of activating a passive state, either alone or with extra resources (active control state) and/or operations (measurement of the control system). By disproving the first possibility and confirming the second one, we show that quantum switch is not a thermodynamic resource in the discussed context, though it can facilitate work extraction given external resources. We discuss our findings by considering specific examples: a qubit system subject to rotations around the x and y axes in the Bloch sphere, as well as general unitaries from the U(2) group; and the system as a quantum harmonic oscillator with displacement operators, as well as with a combination of displacement and squeeze operators.
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Affiliation(s)
- Otavio A D Molitor
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
| | - Łukasz Rudnicki
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
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Céleri LC, Rudnicki Ł. Gauge-Invariant Quantum Thermodynamics: Consequences for the First Law. Entropy (Basel) 2024; 26:111. [PMID: 38392366 PMCID: PMC10888098 DOI: 10.3390/e26020111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2023] [Revised: 01/22/2024] [Accepted: 01/23/2024] [Indexed: 02/24/2024]
Abstract
The universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small systems are considered and fluctuations become important, thermodynamic quantities can be understood in the context of classical stochastic mechanics. A fundamental assumption behind thermodynamics is therefore that of coarse graining, which stems from a substantial lack of control over all degrees of freedom. However, when quantum systems are concerned, one claims a high level of control. As a consequence, information theory plays a major role in the identification of thermodynamic functions. Here, drawing from the concept of gauge symmetry-essential in all modern physical theories-we put forward a new possible intermediate route. Working within the realm of quantum thermodynamics, we explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse graining behind thermodynamics. As a first application of this new framework, we reinterpret quantum work and heat, as well as the role of quantum coherence.
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Affiliation(s)
- Lucas C Céleri
- QPequi Group, Institute of Physics, Federal University of Goiás, Goiânia 74690-900, Brazil
| | - Łukasz Rudnicki
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
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Cusumano S, Rudnicki Ł. Thermodynamics of Reduced State of the Field. Entropy (Basel) 2021; 23:1198. [PMID: 34573823 PMCID: PMC8466179 DOI: 10.3390/e23091198] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/18/2021] [Revised: 08/30/2021] [Accepted: 09/06/2021] [Indexed: 12/02/2022]
Abstract
Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.
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Affiliation(s)
- Stefano Cusumano
- International Center for Theory of Quantum Technologies, University of Gdansk, 80-308 Gdańsk, Poland;
| | - Łukasz Rudnicki
- International Center for Theory of Quantum Technologies, University of Gdansk, 80-308 Gdańsk, Poland;
- Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warszawa, Poland
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Cusumano S, Rudnicki Ł. Comment on "Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries". Phys Rev Lett 2021; 127:028901. [PMID: 34296931 DOI: 10.1103/physrevlett.127.028901] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 06/04/2021] [Indexed: 06/13/2023]
Abstract
In the abstract of [Phys. Rev. Lett. 125, 040601 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.040601] one can read that "[…] to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a 'free energy operator,' defined by F≡H_{W}+β^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and β is the inverse temperature […]." Contrarily to what is presented below Eq. (17) of the Letter, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.
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Affiliation(s)
- Stefano Cusumano
- International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Łukasz Rudnicki
- International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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Rudnicki Ł, Sánchez-Soto LL, Leuchs G, Boyd RW. Fundamental quantum limits in ellipsometry. Opt Lett 2020; 45:4607-4610. [PMID: 32797021 DOI: 10.1364/ol.392955] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Accepted: 07/01/2020] [Indexed: 06/11/2023]
Abstract
We establish the ultimate limits that quantum theory imposes on the accuracy attainable in optical ellipsometry. We show that the standard quantum limit, as usually reached when the incident light is in a coherent state, can be surpassed with the use of appropriate squeezed states and, for tailored beams, even pushed to the ultimate Heisenberg limit.
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Pozas-Kerstjens A, Rabelo R, Rudnicki Ł, Chaves R, Cavalcanti D, Navascués M, Acín A. Bounding the Sets of Classical and Quantum Correlations in Networks. Phys Rev Lett 2019; 123:140503. [PMID: 31702186 DOI: 10.1103/physrevlett.123.140503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Indexed: 06/10/2023]
Abstract
We present a method that allows the study of classical and quantum correlations in networks with causally independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programing, it enables the use of the Navascués-Pironio-Acín hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.
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Affiliation(s)
- Alejandro Pozas-Kerstjens
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Rafael Rabelo
- Instituto de Fisica "Gleb Wataghin," Universidade Estadual de Campinas, CEP 13083-859, Campinas, Brazil
| | - Łukasz Rudnicki
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
- Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Rafael Chaves
- International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitario, Lagoa Nova, Natal-RN 59078-970, Brazil
- School of Science and Technology, Federal University of Rio Grande do Norte, 59078-970 Natal, Brazil
| | - Daniel Cavalcanti
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Miguel Navascués
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Antonio Acín
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain
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Toscano F, Tasca DS, Rudnicki Ł, Walborn SP. Uncertainty Relations for Coarse-Grained Measurements: An Overview. Entropy (Basel) 2018; 20:E454. [PMID: 33265544 PMCID: PMC7512973 DOI: 10.3390/e20060454] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 06/02/2018] [Accepted: 06/06/2018] [Indexed: 12/04/2022]
Abstract
Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.
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Affiliation(s)
- Fabricio Toscano
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21941-972, Brazil
| | - Daniel S. Tasca
- Instituto de Física, Universidade Federal Fluminense, Niteroi 24210-346, Brazil
| | - Łukasz Rudnicki
- Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, Erlangen 91058, Germany
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Warsaw 02-668, Poland
| | - Stephen P. Walborn
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21941-972, Brazil
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Tasca DS, Sánchez P, Walborn SP, Rudnicki Ł. Mutual Unbiasedness in Coarse-Grained Continuous Variables. Phys Rev Lett 2018; 120:040403. [PMID: 29437426 DOI: 10.1103/physrevlett.120.040403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2017] [Revised: 11/09/2017] [Indexed: 06/08/2023]
Abstract
The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.
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Affiliation(s)
- Daniel S Tasca
- Instituto de Física, Universidade Federal Fluminense, Niterói, Rio de Janeiro 24210-346, Brazil
| | - Piero Sánchez
- Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Apartado 1761, Lima, Peru
| | - Stephen P Walborn
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
| | - Łukasz Rudnicki
- Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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Tasca DS, Rudnicki Ł, Gomes RM, Toscano F, Walborn SP. Reliable entanglement detection under coarse-grained measurements. Phys Rev Lett 2013; 110:210502. [PMID: 23745847 DOI: 10.1103/physrevlett.110.210502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2013] [Indexed: 06/02/2023]
Abstract
We derive reliable entanglement witnesses for coarse-grained measurements on continuous variable systems. These witnesses never return a "false positive" for identification of entanglement, under any degree of coarse graining. We show that even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.
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Affiliation(s)
- D S Tasca
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
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Abstract
For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled states and it allows us to construct a family of entanglement measures, we shall call collectibility. As these quantities are experimentally accessible, the approach advocated contributes to the task of experimental quantification of quantum entanglement, while for a three-qubit system it is capable to identify the genuine three-party entanglement.
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Affiliation(s)
- Łukasz Rudnicki
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02-668 Warsaw, Poland.
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