Uniform continuity bounds for information characteristics of quantum channels depending on input dimension and on input energy

Abstract

We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input energy bound (if the input dimension is infinite). We pay a special attention to the case of a multi-mode quantum oscillator as an input system. First we prove continuity bounds for the output conditional mutual information for a single channel and for $n$ copies of a channel. Then we obtain estimates for variation of the output Holevo quantity with respect to simultaneous variations of a channel and of an input ensemble. 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. Finally, we obtain tight and close-to-tight continuity bounds for basic capacities of infinite-dimensional energy-constrained channels with respect to the energy-constrained Bures distance generating the strong convergence of quantum channels.

34 pages, in v.2 we add specifications of all the results for the case of multi-mode quantum oscillator (as input system), in v.3 the diamond-norm topology on the set of channels is replaced by the strong (pointwise) convergence topology, in v.4 the continuity bounds for energy-constrained channel capacities are improved (made tight or close-to-tight), v.5 is the journal version. arXiv admin note: text overlap with arXiv:1604.00568

References in corpus (11)

• Fundamental Limits of Repeaterless Quantum Communications
• General Benchmarks for Quantum Repeaters
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Quantum Capacities of Bosonic Channels
• The structure of degradable quantum channels
• Continuity of quantum channel capacities
• Energy-constrained diamond norms and their use in quantum information theory
• Tight continuity bounds for the quantum conditional mutual information, for the Holevo quantity and for capacities of quantum channels
• Distinguishability measures between ensembles of quantum states
• Adaptation of the Alicki-Fannes-Winter method for the set of states with bounded energy and its use
• Uniform finite-dimensional approximation of basic capacities of energy-constrained channels

Cited by in corpus (18)

• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Continuity of quantum entropic quantities via almost convexity
• Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
• Optimal uniform continuity bound for conditional entropy of classical--quantum states
• 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