Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0107026 · Optics and Spectroscopy

Thermodynamical analogues in quantum information theory

Daniel Rohrlich

Published Sep 1, 2001• 5 citations
arXivHTMLPDF

Abstract

The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to efficiently exploit this resource. We learn how to efficiently exploit entanglement by applying analogues of thermodynamical concepts. These concepts include reversibility, entropy, and the distinction between intensive and extensive quantities. We discuss some of these analogues and show how they lead to a measure of entanglement for pure states. We also ask whether these analogues are more than analogues, and note that, locally, entropy of entanglement is thermodynamical entropy.

DOI
10.1134/1.1405213

Related papers

Entanglement and thermodynamics in general probabilistic theories

Giulio Chiribella, Carlo Maria Scandolo

Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum.More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement.Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories.We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication.Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement.We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system.Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level.As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement.The correspondence is then used to define entanglement measures in the general probabilistic framework.Finally, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).

arXiv:1504.07045•New Journal of Physics•Oct 14, 2015•51 citations

Uniqueness of Entanglement Measure and Thermodynamics

Vlatko Vedral, Elham Kashefi

We apply the axiomatic approach to thermodynamics presented by Giles to derive a unique measure of entanglement for bi-partite pure states. This implies that local manipulations of entanglement in quantum information theory and adiabatic transformations of states in thermodynamics have the same underlying mathematical structure. We discuss possible extensions of our results to mixed and multi-partite states.

arXiv:quant-ph/0112137•Dec 21, 2001•3 citations

Classical information

Vlatko Vedral

Abstract This book deals with the basic concept of information, its importance, and the similarities and differences between classical and quantum information. First, classical information theory and its application to communication are discussed. Quantum mechanics and communication based on the laws of quantum mechanics are then considered. Quantum entanglement, a key resource in quantum communication, is analysed both from the fundamental perspective and from the perspective of its information-processing capability. This book also introduces quantum computation (in the context of the search and factorisation algorithms) and the basics of quantum error correction. Throughout this book, the connections between information theory, thermodynamics, and (quantum) physics are emphasised and discussed. Other topics covered in the book are data compression, related measures of information such as relative entropy, joint entropy, conditional entropy, and mutual information, along with the capacity of a noisy channel.

•Sep 28, 2006•0 citations

Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics

Takahiro Sagawa

In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories including matrix analysis and asymptotic probability theory. The main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it. We focus on both of purely information-theoretic concepts and their physical implications: We present self-contained and rigorous proofs of several fundamental properties of entropies, divergences, and majorization. We also discuss the modern formulations of thermodynamics, especially from the perspectives of stochastic thermodynamics and resource theory of thermodynamics. Resource theory is a recently-developed field as a branch of quantum information theory in order to quantify (energetically or information-theoretically) "useful resources." We show that resource theory has an intrinsic connection to various fundamental ideas of mathematics and information theory. This book is not intended to be a comprehensive review of the field, but would serve as a concise introduction to several important ingredients of the information-theoretic formulation of thermodynamics.

arXiv:2007.09974•Jul 20, 2020•5 citations

Quantum Coarse-Graining: An Information-Theoretic Approach to Thermodynamics

Philippe Faist

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 thermodynamics. With our framework we may determine the minimal work cost of implementing any logical process. In the case of information processing on memory registers with a degenerate Hamiltonian, the answer is given by the max-entropy, a measure of information known from quantum information theory. In the general case, we obtain a new information measure, the "coherent relative entropy", which generalizes both the conditional entropy and the relative entropy. It satisfies a collection of properties which justifies its interpretation as an entropy measure and which connects it to known quantities. We then present how, from our framework, macroscopic thermodynamics emerges by typicality, after singling out an appropriate class of thermodynamic states possessing some suitable reversibility property. A natural thermodynamic potential emerges, dictating possible state transformations, and whose differential describes the physics of the system. The textbook thermodynamics of a gas is recovered as well as the form of the second law relating thermodynamic entropy and heat exchange. Finally, noting that quantum states are relative to the observer, we see that the procedure above gives rise to a natural form of coarse-graining in quantum mechanics: Each observer can consistently apply the formalism of quantum information according to their own fundamental unit of information.

arXiv:1607.03104•Jan 1, 2016•18 citations

Introduction to Information Entropy

Anil Kumar

This is intended to be an introductory book on information entropy. The concept of information theory is too broad to be captured by single definition. The term entropy is used in information theory to describe the amount of uncertainty. The information entropy is a fundamental quantity, related to thermodynamical entropy, which measures the extent of single particle density. The information and entropy both depend upon the choice of probability distribution. Quantum information science will lead to the creation of a quantum computer to solve problem that could not be solved by classical computer. The ideas from information theory have been applied to many problems of science and technology and in other different fields. Quantum Information entropy plays a crucial role in stronger formulation of uncertainty relation. The quantum information entropy of some important potentials is discussed which are widely used in different fields. The information entropy of these potentials is studied in position as well as momentum space and uncertainty relations are verified.

•Oct 19, 2015•0 citations
The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to efficiently exploit this resource. We learn how to efficiently exploit entanglement by applying analogues of thermodynamical concepts. These concepts include reversibility, entropy, and the distinction between intensive and extensive quantities. We discuss some of these analogues and show how they lead to a measure of entanglement for pure states. We also ask whether these analogues are more than analogues, and note that, locally, entropy of entanglement is thermodynamical entropy.
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum.More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement.Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories.We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication.Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement.We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system.Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level.As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement.The correspondence is then used to define entanglement measures in the general probabilistic framework.Finally, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).
Abstract This book deals with the basic concept of information, its importance, and the similarities and differences between classical and quantum information. First, classical information theory and its application to communication are discussed. Quantum mechanics and communication based on the laws of quantum mechanics are then considered. Quantum entanglement, a key resource in quantum communication, is analysed both from the fundamental perspective and from the perspective of its information-processing capability. This book also introduces quantum computation (in the context of the search and factorisation algorithms) and the basics of quantum error correction. Throughout this book, the connections between information theory, thermodynamics, and (quantum) physics are emphasised and discussed. Other topics covered in the book are data compression, related measures of information such as relative entropy, joint entropy, conditional entropy, and mutual information, along with the capacity of a noisy channel.
In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories including matrix analysis and asymptotic probability theory. The main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it. We focus on both of purely information-theoretic concepts and their physical implications: We present self-contained and rigorous proofs of several fundamental properties of entropies, divergences, and majorization. We also discuss the modern formulations of thermodynamics, especially from the perspectives of stochastic thermodynamics and resource theory of thermodynamics. Resource theory is a recently-developed field as a branch of quantum information theory in order to quantify (energetically or information-theoretically) "useful resources." We show that resource theory has an intrinsic connection to various fundamental ideas of mathematics and information theory. This book is not intended to be a comprehensive review of the field, but would serve as a concise introduction to several important ingredients of the information-theoretic formulation of thermodynamics.
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 thermodynamics. With our framework we may determine the minimal work cost of implementing any logical process. In the case of information processing on memory registers with a degenerate Hamiltonian, the answer is given by the max-entropy, a measure of information known from quantum information theory. In the general case, we obtain a new information measure, the "coherent relative entropy", which generalizes both the conditional entropy and the relative entropy. It satisfies a collection of properties which justifies its interpretation as an entropy measure and which connects it to known quantities. We then present how, from our framework, macroscopic thermodynamics emerges by typicality, after singling out an appropriate class of thermodynamic states possessing some suitable reversibility property. A natural thermodynamic potential emerges, dictating possible state transformations, and whose differential describes the physics of the system. The textbook thermodynamics of a gas is recovered as well as the form of the second law relating thermodynamic entropy and heat exchange. Finally, noting that quantum states are relative to the observer, we see that the procedure above gives rise to a natural form of coarse-graining in quantum mechanics: Each observer can consistently apply the formalism of quantum information according to their own fundamental unit of information.
This is intended to be an introductory book on information entropy. The concept of information theory is too broad to be captured by single definition. The term entropy is used in information theory to describe the amount of uncertainty. The information entropy is a fundamental quantity, related to thermodynamical entropy, which measures the extent of single particle density. The information and entropy both depend upon the choice of probability distribution. Quantum information science will lead to the creation of a quantum computer to solve problem that could not be solved by classical computer. The ideas from information theory have been applied to many problems of science and technology and in other different fields. Quantum Information entropy plays a crucial role in stronger formulation of uncertainty relation. The quantum information entropy of some important potentials is discussed which are widely used in different fields. The information entropy of these potentials is studied in position as well as momentum space and uncertainty relations are verified.