The invalidity of a strong capacity for a quantum channel with memory

TL;DR

This paper demonstrates that the strong capacity concept does not universally apply to quantum channels with memory, specifically showing the failure of the strong converse for periodic quantum channels and revealing a scale of capacities based on error probabilities.

Contribution

It proves that the strong converse does not hold for periodic quantum channels, introducing a capacity scale related to error probabilities and challenging previous assumptions.

Findings

Strong converse fails for periodic quantum channels.

Existence of a capacity scale linked to error probability levels.

Similar capacity scale observed in random quantum channels.

Abstract

The strong capacity of a particular channel can be interpreted as a sharp limit on the amount of information which can be transmitted reliably over that channel. To evaluate the strong capacity of a particular channel one must prove both the direct part of the channel coding theorem and the strong converse for the channel. Here we consider the strong converse theorem for the periodic quantum channel and show some rather surprising results. We first show that the strong converse does not hold in general for this channel and therefore the channel does not have a strong capacity. Instead, we find that there is a scale of capacities corresponding to error probabilities between integer multiples of the inverse of the periodicity of the channel. A similar scale also exists for the random channel.