Capacities of quantum Markovian noise for large times

TL;DR

This paper investigates the long-term capacities of quantum Markovian noise channels, revealing that classical and quantum capacities at infinite time are determined by spectral properties and are additive, with improved algorithms for their computation.

Contribution

It introduces a spectral characterization of capacities at infinite time and demonstrates their additivity, along with an improved algorithm for analyzing quantum channels.

Findings

Capacities are characterized by peripheral spectrum properties.

Capacities are additive under tensor products.

An improved algorithm for peripheral subspace computation.

Abstract

Given a quantum Markovian noise model, we study the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical and quantum capacities are characterized by efficiently computable properties of the peripheral spectrum of the quantum channel. In addition, the capacities are additive under tensor product, which implies in the language of Shannon theory that the one-shot and the asymptotic i.i.d. capacities are the same. We also provide an improved algorithm for computing the structure of the peripheral subspace of a quantum channel, which might be of independent interest.