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Thermodynamics of Quantum Information
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Thermodynamics of Quantum Information

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (15 September 2021) | Viewed by 22989

Special Issue Editors

Dr. Sebastian Deffner

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Guest Editor
Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA
Interests: Brownian motion; quantum thermodynamics; theoretical physics; statistical physics; quantum control; quantum speed limit; shortcuts to adiabaticity; quantum information theory; foundations of physics
Special Issues, Collections and Topics in MDPI journals
Dr. Frederico Brito

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Guest Editor
Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos 13560‐970, SP, Brazil
Interests: open quantum systems; quantum thermodynamics; quantum computation

Special Issue Information

Dear Colleagues,

It is a commonly accepted creed that the development of practically useful quantum computers might revolutionize how we store, communicate, and process information. The so-called “quantum supremacy” of these new information technologies originates in the observation that quantum computers can perform certain tasks exponentially faster than any classical hardware. More specifically, in each moment, a quantum computer has access to exponentially more logical states, and thus, a quantum computer has the potential to process exponentially more information per logical operation. However, we have known since the 1960s that information is physical and that its processing consumes thermodynamic resources. Hence, we need to consider whether quantum computers will also necessitate exponentially more energy to operate than any classical computer to sustain any possible quantum advantage.

To elucidate this fundamental question, the development of a comprehensive framework of the Thermodynamics of Quantum Information appears urgent and instrumental. This is a further example of the universality of thermodynamic concepts and real-world ramifications of the steadfast framework of the theory. This Special Issue will reflect the current, rich scenario of methods, concepts, and applications of quantum thermodynamics applied to quantum computing.

Dr. Sebastian Deffner
Dr. Frederico Brito
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum thermodynamics
  • Quantum information
  • Quantum computing
  • Quantum error correction
  • Quantum heat engines
  • Quantum Maxwell demons

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Related Special Issues

Published Papers (6 papers)

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Research

8 pages, 269 KiB  
Article
Fluctuations in Extractable Work and Bounds on the Charging Power of Quantum Batteries
by Shang-Yung Wang
Entropy 2021, 23(11), 1455; https://doi.org/10.3390/e23111455 - 1 Nov 2021
Cited by 2 | Viewed by 1920
Abstract
Motivated by a recent disagreement about the claim that fluctuations in the free energy operator bound the charging power of a quantum battery, we present a critical analysis of the original derivation. The analysis shows that the above claim does not hold for [...] Read more.
Motivated by a recent disagreement about the claim that fluctuations in the free energy operator bound the charging power of a quantum battery, we present a critical analysis of the original derivation. The analysis shows that the above claim does not hold for both closed- and open-system dynamics. Our results indicate that the free energy operator is not a consistent quantifying operator for the work content of a charging quantum battery. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
13 pages, 314 KiB  
Article
Quantum and Classical Ergotropy from Relative Entropies
by Akira Sone and Sebastian Deffner
Entropy 2021, 23(9), 1107; https://doi.org/10.3390/e23091107 - 25 Aug 2021
Cited by 17 | Viewed by 4283
Abstract
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect [...] Read more.
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
13 pages, 1027 KiB  
Article
Quantum Euler Relation for Local Measurements
by Akram Touil, Kevin Weber and Sebastian Deffner
Entropy 2021, 23(7), 889; https://doi.org/10.3390/e23070889 - 13 Jul 2021
Cited by 1 | Viewed by 3385
Abstract
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects [...] Read more.
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
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43 pages, 499 KiB  
Article
Currencies in Resource Theories
by Lea Kraemer and Lídia del Rio
Entropy 2021, 23(6), 755; https://doi.org/10.3390/e23060755 - 15 Jun 2021
Cited by 3 | Viewed by 2671
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. [...] Read more.
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. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
16 pages, 1849 KiB  
Article
Quantum Work Statistics with Initial Coherence
by María García Díaz, Giacomo Guarnieri and Mauro Paternostro
Entropy 2020, 22(11), 1223; https://doi.org/10.3390/e22111223 - 27 Oct 2020
Cited by 18 | Viewed by 3677
Abstract
The two-point measurement scheme for computing the thermodynamic work performed on a system requires it to be initially in equilibrium. The Margenau–Hill scheme, among others, extends the previous approach to allow for a non-equilibrium initial state. We establish a quantitative comparison between both [...] Read more.
The two-point measurement scheme for computing the thermodynamic work performed on a system requires it to be initially in equilibrium. The Margenau–Hill scheme, among others, extends the previous approach to allow for a non-equilibrium initial state. We establish a quantitative comparison between both schemes in terms of the amount of coherence present in the initial state of the system, as quantified by the l1-coherence measure. We show that the difference between the two first moments of work, the variances of work, and the average entropy production obtained in both schemes can be cast in terms of such initial coherence. Moreover, we prove that the average entropy production can take negative values in the Margenau–Hill framework. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
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11 pages, 2235 KiB  
Article
Otto Engine: Classical and Quantum Approach
by Francisco J. Peña, Oscar Negrete, Natalia Cortés and Patricio Vargas
Entropy 2020, 22(7), 755; https://doi.org/10.3390/e22070755 - 9 Jul 2020
Cited by 19 | Viewed by 4538
Abstract
In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or [...] Read more.
In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or equal to its quantum counterpart, independent of the working substance. In the classical case, this is due to the fact that the working substance is always in thermodynamic equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic paths. We apply this analysis to the case of a two-level system, finding that the work and efficiency in both the Otto’s quantum and classical cycles are identical, regardless of the working substance, and we obtain similar results for a multilevel system where a linear relationship between the spectrum of energies of the working substance and the external magnetic field is fulfilled. Finally, we show an example of a three-level system in which we compare two zones in the entropy diagram as a function of temperature and magnetic field to find which is the most efficient region when performing a thermodynamic cycle. This work provides a practical way to look for temperature and magnetic field zones in the entropy diagram that can maximize the power extracted from an Otto magnetic engine. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
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