Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity

Abstract

The fully quantum reverse Shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state, while also allowing for an arbitrary amount of shared entanglement of an arbitrary form. Turning this theorem around establishes a strong converse for the entanglement-assisted classical capacity of any quantum channel. This paper proves the strong converse for entanglement-assisted capacity by a completely different approach and identifies a bound on the strong converse exponent for this task. Namely, we exploit the recent entanglement-assisted "meta-converse" theorem of Matthews and Wehner, several properties of the recently established sandwiched Renyi relative entropy (also referred to as the quantum Renyi divergence), and the multiplicativity of completely bounded $p$-norms due to Devetak et al. The proof here demonstrates the extent to which the Arimoto approach can be helpful in proving strong converse theorems, it provides an operational relevance for the multiplicativity result of Devetak et al., and it adds to the growing body of evidence that the sandwiched Renyi relative entropy is the correct quantum generalization of the classical concept for all $\alpha >1$.

arXiv comment21 pages, final version accepted for publication in Communications in Mathematical Physics

References in corpus (36)

• On quantum Renyi entropies: a new generalization and some properties
• Distance measures to compare real and ideal quantum processes
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• The Quantum Chernoff Bound
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Correcting Quantum Errors with Entanglement
• Asymptotic Error Rates in Quantum Hypothesis Testing
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Quantum Reverse Shannon Theorem
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Strong Converse to the Quantum Channel Coding Theorem
• Unconditional security from noisy quantum storage
• On the quantum Renyi relative entropies and related capacity formulas
• Entanglement can enhance the distinguishability of entanglement-breaking channels
• Catalytic quantum error correction
• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• Finite blocklength converse bounds for quantum channels
• On entanglement-assisted classical capacity
• Reverse Coherent Information
• Entanglement-assisted quantum turbo codes
• A strong converse for classical channel coding using entangled inputs
• Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• High performance entanglement-assisted quantum LDPC codes need little entanglement
• A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
• Quantum rate distortion, reverse Shannon theorems, and source-channel separation
• A limit of the quantum Renyi divergence
• Quantum Feedback Channels
• "Pretty strong" converse for the quantum capacity of degradable channels
• Two-message quantum interactive proofs are in PSPACE
• Simpler semidefinite programs for completely bounded norms
• Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem
• A relation between completely bounded norms and conjugate channels

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• Optimized quantum f-divergences and data processing
• Rényi squashed entanglement, discord, and relative entropy differences
• Investigating Properties of a Family of Quantum Renyi Divergences
• Temperature driven quenches in the Ising model: appearance of negative Rényi mutual information
• Strong converse theorems using Rényi entropies
• Renyi relative entropies of quantum Gaussian states
• Rényi generalizations of quantum information measures
• Rényi Mutual Information in Quantum Field Theory
• Quantum Markov chains, sufficiency of quantum channels, and Renyi information measures
• Capacity Estimates via comparison with TRO channels
• Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
• Relative entropy for von Neumann subalgebras
• On zero-error communication via quantum channels in the presence of noiseless feedback
• Recoverability for optimized quantum $f$-divergences
• Moderate deviation expansion for fully quantum tasks
• Quantum reading capacity: General definition and bounds
• Quantum realism: axiomatization and quantification
• Refined Strong Converse for the Constant Composition Codes
• Reliability Function of Classical-Quantum Channels
• Quantifying the unextendibility of entanglement
• Reliable Simulation of Quantum Channels: the Error Exponent
• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• Capacity Bounds via Operator Space Methods
• Lower Bounds on Error Exponents via a New Quantum Decoder
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• Strong Converse Exponent for Entanglement-Assisted Communication
• Strong converse for the quantum capacity of the erasure channel for almost all codes
• A strong converse for the quantum state merging protocol
• Capacity of Diffusion based Molecular Communication Networks over LTI-Poisson Channels
• Quantum channel coding: Approximation algorithms and strong converse exponents
• An upper bound on quantum capacity of unital channels
• Additivity and chain rules for quantum entropies via multi-index Schatten norms
• Retrocausal capacity of a quantum channel: Communicating through noisy closed timelike curves
• Quantum information theory and Fourier multipliers on quantum groups
• A fixed-point algorithm for matrix projections with applications in quantum information