Superadditivity of the Classical Capacity with Limited Entanglement Assistance

Abstract

Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the entanglement-assisted classical capacity for any channel is additive, making entanglement across channel uses unnecessary. If the entanglement assistance is limited, the picture is much more unclear. Suppose the classical capacity is superadditive, then the classical capacity with limited entanglement assistance could retain superadditivity by continuity arguments. If the classical capacity is additive, it is unknown if superadditivity can still be developed with limited entanglement assistance. We show this is possible, by providing an example. We construct a channel for which, the classical capacity is additive, but that with limited entanglement assistance can be superadditive. This shows entanglement plays a weird role in communication and we still understand very little about it.

13 pages

References in corpus (4)

• Degenerate Quantum Codes for Pauli Channels
• Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement
• Simultaneous classical-quantum capacities of quantum multiple access channels
• Simplification of additivity conjecture in quantum information theory

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• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
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• Simultaneous superadditivity of the direct and complementary channel capacities
• Permutation Enhances Classical Communication Assisted by Entangled States