Bounding the forward classical capacity of bipartite quantum channels

Abstract

We introduce various measures of forward classical communication for bipartite quantum channels. Since a point-to-point channel is a special case of a bipartite channel, the measures reduce to measures of classical communication for point-to-point channels. As it turns out, these reduced measures have been reported in prior work of Wang et al. on bounding the classical capacity of a quantum channel. As applications, we show that the measures are upper bounds on the forward classical capacity of a bipartite channel. The reduced measures are upper bounds on the classical capacity of a point-to-point quantum channel assisted by a classical feedback channel. Some of the various measures can be computed by semi-definite programming.

v3: 29 pages, 6 figures, final version accepted for publication in IEEE Transactions on Information Theory

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• Semidefinite programming relaxations for quantum correlations
• The platypus of the quantum channel zoo
• Some continuity properties of quantum Rényi divergences
• Quantum algorithms for matrix geometric means
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States
• Optimized protocols for duplex quantum transduction
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Unextendible entanglement of quantum channels
• Extendibility limits quantum-secured communication and key distillation
• Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions