Generic nonadditivity of quantum capacity in simple channels

Abstract

Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to super-additivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of super-additive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display super-additivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display super-additivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in the companion paper [IEEE Trans. Inf. Theory 69(6), pp. 3825-3849, 2023; arXiv:2202.08380], our results on super-additivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, super-additivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves super-additivity in all examples. Our results show that super-additivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity.

Comments: 25 pages, 9 figures. v2: matches published version. See also the companion paper arXiv:2202.08380

References in corpus (13)

• Quantum Communication With Zero-Capacity Channels
• Degenerate Quantum Codes for Pauli Channels
• The structure of degradable quantum channels
• Unbounded number of channel uses are required to see quantum capacity
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• The quantum capacity with symmetric side channels
• New lower bounds on the non-zero capacity of Pauli Channels
• Extensive nonadditivity of privacy
• For quantum information, two wrongs can make a right
• Can non-private channels transmit quantum information?
• Activation and superactivation of single-mode Gaussian quantum channels
• The platypus of the quantum channel zoo
• Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms

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• Multipartite entanglement to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses
• Towards a resolution of the spin alignment problem
• Optimal one-shot entanglement sharing
• Noise is resource-contextual in quantum communication
• Additivity of quantum capacities in simple non-degradable quantum channels
• Simultaneous superadditivity of the direct and complementary channel capacities
• Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory
• Refining Ky Fan's majorization relation with linear programming
• Information storage and transmission under Markovian noise