Sequential transmission at short times

TL;DR

This paper demonstrates that quantum information can be transmitted and entanglement preserved over sequential quantum channels by combining noise with quantum error correction, with transmission rates linked to the channels' spectral properties.

Contribution

It introduces a lower bound on one-shot quantum capacity in a sequential setting and relates transmission properties to the spectral characteristics of composed channels.

Findings

Transmission rate depends on the spectrum of the channel sequence.

Maximum error in transmission can be bounded by the noise model.

Derived an exact error bound for the pure-loss channel.

Abstract

We show that it is possible to transmit and preserve information at short time scales over an n-fold composition of quantum channels $(\Xi^n)_{n \in \mathbb{N}}$ modelled as a discrete quantum Markov semigroup, long enough to generate entanglement at some finite $n$. This is achieved by interspersing the action of noise with quantum error correction in succession. We show this by means of a non-trivial lower bound on the one-shot quantum capacity in the sequential setting as a function of $n$, in an attempt to model a linear quantum network and assess its capabilities to distribute entanglement. Intriguingly, the rate of transmission of such a network turns out to be a property of the spectrum of the channels composed in sequence, and the maximum possible error in transmission can be bounded as a function of the noise model only. As an application, we derive an exact error bound for the infinite dimensional pure-loss channel believed to be the dominant source of noise in networks precluding the distribution of entanglement. We exemplify our results by analysing the amplitude damping channel and its bosonic counterpart.