Continuity of quantum channel capacities

Abstract

We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical capacity, quantum capacity, and private classical capacity are continuous, with the variation on arguments epsilon apart bounded by a simple function of epsilon and the channel's output dimension. Our main tool is an upper bound of the variation of output entropies of many copies of two nearby channels given the same initial state; the bound is linear in the number of copies. Our second proof is concerned with the quantum capacities in the presence of free backward or two-way public classical communication. These capacities are proved continuous on the interior of the set of non-zero capacity channels by considering mutual simulation between similar channels.

12 pages, Revised according to referee's suggestions

References in corpus (14)

• Mixed State Entanglement and Quantum Error Correction
• The capacity of the noisy quantum channel
• "Squashed Entanglement" - An Additive Entanglement Measure
• Capacities of Quantum Erasure Channels
• Continuity of quantum conditional information
• Superdense coding of quantum states
• Degenerate Quantum Codes for Pauli Channels
• Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
• Continuity bounds for entanglement
• Multiplicativity of completely bounded p-norms implies a new additivity result
• Structured Codes Improve the Bennett-Brassard-84 Quantum Key Rate
• The Holevo capacity of infinite dimensional channels and the additivity problem
• The quantum capacity is properly defined without encodings
• How to correct small quantum errors

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