The Quantum Reverse Shannon Theorem based on One-Shot Information Theory

Abstract

The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel's entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.

30 pages, 4 figures, published version

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Cited by in corpus (107)

• Quantum Resource Theories
• Quantum channels and memory effects
• Distributed Channel Synthesis
• Quantum Reverse Shannon Theorem
• Exponential Decay of Correlations Implies Area Law
• One-shot decoupling
• One-shot coherence distillation
• One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
• Quantum message compression with applications
• Leading order corrections to the quantum extremal surface prescription
• Renyi generalizations of the conditional quantum mutual information
• The information-theoretic costs of simulating quantum measurements
• Entanglement Cost of Quantum Channels
• Application of the Resource Theory of Channels to Communication Scenarios
• Resource theory of asymmetric distinguishability for quantum channels
• Limits to catalysis in quantum thermodynamics
• Semidefinite programming strong converse bounds for classical capacity
• Strong converse rates for quantum communication
• No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
• Quantum Channel Simulation and the Channel's Smooth Max-Information
• Quantum rate distortion, reverse Shannon theorems, and source-channel separation
• Semidefinite programming relaxations for quantum correlations
• Smooth Max-Information as One-Shot Generalization for Mutual Information
• On the Second-Order Asymptotics for Entanglement-Assisted Communication
• One-shot entanglement-assisted quantum and classical communication
• Thermodynamic Capacity of Quantum Processes
• Catalysis of entanglement and other quantum resources
• A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
• Entanglement cost and quantum channel simulation
• Entropy of a quantum channel
• Semidefinite programming converse bounds for quantum communication
• Identifying the Information Gain of a Quantum Measurement
• Non-asymptotic assisted distillation of quantum coherence
• Catalytic Decoupling of Quantum Information
• One-shot lossy quantum data compression
• Quantum rate distortion coding with auxiliary resources
• On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• Strong converse theorems using Rényi entropies
• On Composite Quantum Hypothesis Testing
• One-Shot Manipulation of Dynamical Quantum Resources
• Smooth Entropy Bounds on One-Shot Quantum State Redistribution
• All states are universal catalysts in quantum thermodynamics
• "Pretty strong" converse for the quantum capacity of degradable channels
• Asymptotic performance of port-based teleportation
• Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Semidefinite programming hierarchies for constrained bilinear optimization
• Approximate Quantum Error Correction Revisited: Introducing the Alpha-bit
• Entanglement-assisted private communication over quantum broadcast channels
• A generalized quantum Slepian-Wolf
• Partially smoothed information measures
• Computable Rényi mutual information: Area laws and correlations
• Convex-split and hypothesis testing approach to one-shot quantum measurement compression and randomness extraction
• Quantum Rate-Distortion Coding of Relevant Information
• One-shot holography
• A one-shot achievability result for quantum state redistribution
• Conditional Decoupling of Quantum Information
• de Finetti reductions for correlations
• Quantum non-malleability and authentication
• The Communication Value of a Quantum Channel
• Approximate tensorization of the relative entropy for noncommuting conditional expectations
• Reversibility of quantum resources through probabilistic protocols
• On zero-error communication via quantum channels in the presence of noiseless feedback
• Characteristics of Universal Embezzling Families
• Markovianizing Cost of Tripartite Quantum States
• Moderate deviation expansion for fully quantum tasks
• Beyond islands: A free probabilistic approach
• Thermodynamic Implementations of Quantum Processes
• One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information
• Efficient methods for one-shot quantum communication
• Weak approximate unitary designs and applications to quantum encryption
• Communication Cost of Quantum Processes
• Separation between quantum Lovász number and entanglement-assisted zero-error classical capacity
• Communication Complexity of One-Shot Remote State Preparation
• Channel Simulation: Finite Blocklengths and Broadcast Channels
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Complete Characterization of Entanglement Embezzlement
• Relativistic Quantum Fields Are Universal Entanglement Embezzlers
• One-Shot Hybrid State Redistribution
• Decomposition Rules for Quantum Rényi Mutual Information with an Application to Information Exclusion Relations
• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• One-shot quantum state exchange
• Teleportation with Embezzling Catalysts
• Reliable Simulation of Quantum Channels: the Error Exponent
• Quantum State Merging for Arbitrarily Small-Dimensional Systems
• Computable lower bounds on the entanglement cost of quantum channels
• On the quantum no-signalling assisted zero-error classical simulation cost of non-commutative bipartite graphs
• Cone-Restricted Information Theory
• Strong Converse Exponent for Entanglement-Assisted Communication
• Noisy quantum state redistribution with promise and the Alpha-bit
• Shadow Simulation of Quantum Processes
• On relating one-way classical and quantum communication complexities
• State transfer with quantum side information
• Chain rules for quantum channels
• Efficient achievability for quantum protocols using decoupling theorems
• Postselected communication over quantum channels
• Communication with Quantum Catalysts
• Multipartite Embezzlement of Entanglement
• Area laws and tensor networks for maximally mixed ground states
• Expected communication cost of distributed quantum tasks
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• One-Shot Distributed Source Simulation: As Quantum as it Can Get
• Intersection and union of subspaces with applications to communication over authenticated classical-quantum channels and composite hypothesis testing
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Tight relations and equivalences between smooth relative entropies
• On the Entanglement Cost of One-Shot Compression
• One-shot Multiple Access Channel Simulation