Forgetfulness of continuous Markovian quantum channels

TL;DR

This paper extends the concept of forgetfulness to continuous Markovian quantum channels, enabling the analysis of quantum memory channels with Markovian noise and calculating their capacities.

Contribution

It introduces a weakened form of forgetfulness for continuous channels and demonstrates its application to bosonic memory channels with additive noise.

Findings

Channel capacities can be computed using memoryless results

Weak-forgetfulness helps analyze Markovian quantum channels

Method applies to bosonic channels with additive noise

Abstract

The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak-forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.