A reversible theory of entanglement and its relation to the second law

Abstract

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)], and in stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein's Lemma proved in [Brandao and Plenio, Commun. Math. 295, 791 (2010)], giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.

21 pages. revised version

References in corpus (7)

• Quantum Communication With Zero-Capacity Channels
• Quantifying Entanglement with Witness Operators
• Entanglement Theory and the Second Law of Thermodynamics
• A Generalization of Quantum Stein's Lemma
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• Classical simulatability, entanglement breaking, and quantum computation thresholds
• Remarks on the equivalence of full additivity and monotonicity for the entanglement cost

Cited by in corpus (66)

• Quantifying Coherence
• Quantum Coherence as a Resource
• Quantum Resource Theories
• The general structure of quantum resource theories
• Faithful Squashed Entanglement
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• The resource theory of steering
• Converse bounds for private communication over quantum channels
• Entanglement and coherence in quantum state merging
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Operational Resource Theory of Quantum Channels
• A Generalization of Quantum Stein's Lemma
• A resource theory of entanglement with a unique multipartite maximally entangled state
• Relative Entropy Bounds on Quantum, Private and Repeater Capacities
• Axiomatic relation between thermodynamic and information-theoretic entropies
• Quantum Jarzynski Equality in Open Quantum Systems from the One-Time Measurement Scheme
• Catalysis of entanglement and other quantum resources
• No second law of entanglement manipulation after all
• Relative entropy and squashed entanglement
• Logarithmic coherence: Operational interpretation of ${\ell }_1$-norm coherence
• On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• The first law of general quantum resource theories
• Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
• One-Shot Manipulation of Dynamical Quantum Resources
• Tight constraints on probabilistic convertibility of quantum states
• One-shot entanglement distillation beyond local operations and classical communication
• Completing the Grand Tour of asymptotic quantum coherence manipulation
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Disentanglement Cost of Quantum States
• Virtual quantum resource distillation
• On convex optimization problems in quantum information theory
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Quantum data hiding with continuous variable systems
• Work and Heat Value of Bound Entanglement
• Reversibility of quantum resources through probabilistic protocols
• A solution of the generalised quantum Stein's lemma
• Quantum Coherence: Reciprocity and Distribution
• Distillable entanglement under dually non-entangling operations
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• One-shot manipulation of entanglement for quantum channels
• Postselected quantum hypothesis testing
• Entanglement manipulation and distillability beyond LOCC
• Maximally entangled mixed states for a fixed spectrum do not always exist
• No-go theorem for entanglement distillation using catalysis
• Simple Bounds for One-shot Pure-State Distillation in General Resource Theories
• Local Transformations of Multiple Multipartite States
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
• Second Law of Entanglement Manipulation with Entanglement Battery
• Continuity of entropies via integral representations
• An Extention of Entanglement Measures for Pure States
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• Continuity of the relative entropy of resource
• Computable lower bounds on the entanglement cost of quantum channels
• Black Box Work Extraction and Composite Hypothesis Testing
• One-shot manipulation of coherence in dynamic quantum resource theory
• Role of matter coherence in entanglement due to gravity
• Detecting coherence with respect to general quantum measurements
• Asymptotic quantification of entanglement with a single copy
• Second Law of Entanglement Dynamics for the Non-Asymptotic Regime
• Assessing thermalization and estimating the Hamiltonian with output data only
• Multipartite entanglement theory with entanglement-nonincreasing operations
• Tight relations and equivalences between smooth relative entropies
• The entangling power of non-entangling channels
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach
• Nonexistence of maximally entangled mixed states for a fixed spectrum