The Communication Value of a Quantum Channel

Abstract

There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional min-entropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.

References in corpus (40)

• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Conditions for a class of entanglement transformations
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• The operational meaning of min- and max-entropy
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Entanglement Measures under Symmetry
• A complete family of separability criteria
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Quantum Reverse Shannon Theorem
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Counterexample to an additivity conjecture for output purity of quantum channels
• The geometric measure of entanglement for symmetric states
• Finite blocklength converse bounds for quantum channels
• Iterative Optimization of Quantum Error Correcting Codes
• On entanglement-assisted classical capacity
• On the power of PPT-preserving and non-signalling codes
• Entanglement Cost of Quantum Channels
• Application of the Resource Theory of Channels to Communication Scenarios
• Zero-error channel capacity and simulation assisted by non-local correlations
• Semidefinite programming strong converse bounds for classical capacity
• Dephrasure channel and superadditivity of coherent information
• 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
• No-hypersignaling principle
• Classical information storage in an $n$-level quantum system
• Entanglement of a bipartite channel
• Entanglement cost and quantum channel simulation
• Quantum Error Correction via Convex Optimization
• Entanglement of the Antisymmetric State
• On converse bounds for classical communication over quantum channels
• Reduced State Uniquely Defines Groverian Measure of Original Pure State
• Communication of partial ignorance with qubits
• On entanglement assistance to a noiseless classical channel
• Communication tasks in operational theories
• Certifying the Classical Simulation Cost of a Quantum Channel
• On the quantum no-signalling assisted zero-error classical simulation cost of non-commutative bipartite graphs

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• Retrocausal capacity of a quantum channel: Communicating through noisy closed timelike curves
• The signaling dimension in generalized probabilistic theories