Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel

Abstract

The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: the capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is non-convex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.

8 pages, 2 figures

References in corpus (4)

• Quantum Communication With Zero-Capacity Channels
• Unbounded number of channel uses are required to see quantum capacity
• Extensive nonadditivity of privacy
• Can non-private channels transmit quantum information?

Cited by in corpus (5)

• Holevo Capacity of Discrete Weyl Channels
• Quantum-enabled communication without a phase reference
• Heralded Channel Holevo Superadditivity Bounds from Entanglement Monogamy
• Noise is resource-contextual in quantum communication
• Simultaneous superadditivity of the direct and complementary channel capacities