Continuity bounds for information characteristics of quantum channels depending on input dimension

Abstract

We show how to use properties of the quantum conditional mutual information to obtain continuity bounds for information characteristics of quantum channels depending on their input dimension. First we prove tight estimates for variation of the output Holevo quantity with respect to simultaneous variations of a channel and of an input ensemble. Then we obtain tight continuity bounds for output conditional mutual information for a single channel and for $n$ copies of a channel. As a result tight and close-to-tight continuity bounds for basic capacities of quantum channels depending on the input dimension are obtained. They complement the Leung-Smith continuity bounds depending on the output dimension.

18 pages, preliminary version, any comments are welcome. arXiv admin note: text overlap with arXiv:1512.09047

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• Optimal tests for continuous-variable quantum teleportation and photodetectors
• Advanced Alicki-Fannes-Winter method for energy-constrained quantum systems and its use
• Characterizing the performance of continuous-variable Gaussian quantum gates
• Continuity of characteristics of composite quantum systems
• General Continuity Bounds for Quantum Relative Entropies
• Operator E-norms and their use
• Optimal gain sensing of quantum-limited phase-insensitive amplifiers
• Infinite-Dimensional Programmable Quantum Processors
• On lower semicontinuity of the quantum conditional mutual information and its corollaries
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• Correlation measures of a quantum state and information characteristics of a quantum channel
• Continuity bounds for quantum entropies arising from a fundamental entropic inequality
• Optimal form of the Kretschmann-Schlingemann-Werner theorem for energy-constrained quantum channels and operations
• On quantum states with a finite-dimensional approximation property