Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels

TL;DR

This paper establishes a strong converse theorem for the classical capacity of entanglement-breaking quantum channels with classical feedback, showing the capacity boundary is sharp and providing bounds on success probability decay.

Contribution

It proves a strong converse for entanglement-breaking channels with feedback and derives bounds on success probability decay rates using sandwiched Renyi relative entropy.

Findings

Strong converse theorem for entanglement-breaking channels with feedback.

Bound on the exponential decay rate of success probability.

Method applicable to quantum channels with classical feedback without entangled encoding.

Abstract

Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled encoding schemes, but this is not always the case. In this paper, we prove that a strong converse theorem holds for the classical capacity of an entanglement-breaking channel even when it is assisted by a classical feedback link from the receiver to the transmitter. In doing so, we identify a bound on the strong converse exponent, which determines the exponentially decaying rate at which the success probability tends to zero, for a sequence of codes with communication rate exceeding capacity. Proving a strong converse, along with an achievability theorem, shows that the classical capacity is a sharp boundary between reliable and unreliable communication regimes. One of the main tools in our proof is the sandwiched Renyi relative entropy. The same method of proof is used to derive an exponential bound on the success probability when communicating over an arbitrary quantum channel assisted by classical feedback, provided that the transmitter does not use entangled encoding schemes.