Entropic singularities give rise to quantum transmission

Abstract

When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity -- a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel's coherent information. A corollary of this theorem gives a simple dimensional test for a channel's capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.

20 pages, 5 figures, comments are welcome, v2: matches published version

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Cited by in corpus (13)

• Generic nonadditivity of quantum capacity in simple channels
• Detecting positive quantum capacities of quantum channels
• The platypus of the quantum channel zoo
• Bounding quantum capacities via partial orders and complementarity
• Quantum channels that destroy negative conditional entropy
• Coherent information of a quantum channel or its complement is generically positive
• Fully undistillable quantum states are separable
• Optimal one-shot entanglement sharing
• Five Starter Pieces: Quantum Information Science via Semi-definite Programs
• Multipartite entanglement to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses
• Bounding the quantum capacity with flagged extensions
• Noise is resource-contextual in quantum communication
• Additivity of quantum capacities in simple non-degradable quantum channels