Information transmission under Markovian noise

TL;DR

This paper investigates the limits of information transmission through quantum channels with Markovian noise, providing bounds on capacities for classical, quantum, and private information in finite time settings.

Contribution

It introduces bounds on one-shot transmission capacities of quantum channels under Markovian noise based on the channel's peripheral structure.

Findings

Derived upper and lower bounds for transmission capacities

Analyzed classical, quantum, and private information transmission

Connected capacity bounds to the structure of the channel's peripheral space

Abstract

We consider an open quantum system undergoing Markovian dynamics, the latter being modelled by a discrete-time quantum Markov semigroup $(\Phi^n)_{n \in {\mathbb{N}}}$, resulting from the action of sequential uses of a quantum channel $\Phi$, with $n \in {\mathbb{N}}$ being the discrete time parameter. We find upper and lower bounds on the one-shot $\epsilon$-error information transmission capacities of $\Phi^n$ for a finite time $n\in \mathbb{N}$ and $\epsilon \in [0,1)$ in terms of the structure of the peripheral space of the channel $\Phi$. We consider transmission of $(i)$ classical information (both in the unassisted and entanglement-assisted settings); $(ii)$ quantum information and $(iii)$ private classical information.