The strong converse theorem for the product-state capacity of quantum channels with ergodic Markovian memory

TL;DR

This paper proves the strong converse theorem for the product-state capacity of quantum channels with ergodic Markovian memory, establishing the ultimate limit of reliable quantum communication over such channels.

Contribution

It is the first to establish the strong converse for the product-state capacity of quantum channels with ergodic Markovian memory.

Findings

Strong converse holds for quantum channels with ergodic Markovian memory.

Error probability converges to 1 when coding above capacity.

Confirms the capacity as the ultimate reliable communication limit.

Abstract

Establishing the strong converse theorem for a communication channel confirms that the capacity of that channel, that is, the maximum achievable rate of reliable information communication, is the ultimate limit of communication over that channel. Indeed, the strong converse theorem for a channel states that coding at a rate above the capacity of the channel results in the convergence of the error to its maximum value 1 and that there is no trade-off between communication rate and decoding error. Here we prove that the strong converse theorem holds for the product-state capacity of quantum channels with ergodic Markovian correlated memory.