Quantum Coarse-Graining: An Information-theoretic Approach to thermodynamics

@article{Faist2016QuantumCA,
  title={Quantum Coarse-Graining: An Information-theoretic Approach to thermodynamics},
  author={Philippe Faist},
  journal={arXiv: Quantum Physics},
  year={2016}
}
  • P. Faist
  • Published 11 July 2016
  • Physics
  • arXiv: Quantum Physics
We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on this gap. We then introduce a fully information-theoretic framework generalizing the above by making further abstraction of physical quantities such as energy. It is technically convenient to work with and reproduces known results for finite-size quantum… 
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References

SHOWING 1-10 OF 272 REFERENCES
Recoverability in quantum information theory
  • M. Wilde
  • Computer Science
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2015
TLDR
If the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other.
Resource theory of quantum states out of thermal equilibrium.
TLDR
It is shown that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sub linear amount of classical communication required for entanglement dilution.
A framework for non-asymptotic quantum information theory
TLDR
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography, and introduces the purified distance, a novel metric for unnormalized quantum states, and explores various properties of these entropies, including data-processing inequalities, chain rules and their classical limits.
Thermodynamics of Quantum Information Systems — Hamiltonian Description
TLDR
This work proves the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at the cost of entropy of the system, and derives Landauer's principle as a consequence of the second law within the considered model.
A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
TLDR
The derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: the one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems.
Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
TLDR
This work defines a resource-theory model for thermodynamic exchanges of noncommuting observables and investigates the thermal state of the grand canonical ensemble, which is expected to be the equilibrium point of typical dynamics.
Reversible Framework for Quantum Resource Theories.
TLDR
The general structure of QRTs is discussed, and it is shown that under a few assumptions, a QRT is asymptotically reversible if its set of allowed operations is maximal, that is, if the allowed operations are the set of all operations that do not generate (asymptotical) a resource.
Extracting work from quantum systems
We consider the task of extracting work from quantum systems in the resource theory perspective of thermodynamics, where free states are arbitrary thermal states, and allowed operations are energy
Trading coherence and entropy by a quantum Maxwell demon
The second law of thermodynamics states that the entropy of a closed system is nondecreasing. Discussing the second law in the quantum world poses different challenges and provides different
Approximate reversibility in the context of entropy gain, information gain, and complete positivity
TLDR
This paper applies and extends results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic disturbance, and complete positivity of open quantum systems dynamics.
...
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