Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy

Abstract

We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer systems, we show, using permutation symmetry and a de Finetti reduction, how the random coding capacity (classical and quantum) of the QAVC is reduced to the capacity of a naturally associated compound channel, which is obtained by restricting the jammer to i.i.d. input states. Furthermore, we demonstrate that the shared randomness required is at most logarithmic in the block length, using a random matrix tail bound. This implies a dichotomy theorem: either the classical capacity of the QAVC is zero, and then also the quantum capacity is zero, or each capacity equals its random coding variant.

5 pages, ISIT format (IEEEtra.cls)

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Cited by in corpus (4)

• Fault-tolerant Coding for Quantum Communication
• Fault-tolerant Coding for Entanglement-Assisted Communication
• Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks
• Classical capacities of memoryless but not identical quantum channels