Quantum Capacity Approaching Codes for the Detected-Jump Channel

TL;DR

This paper presents a coding scheme for the detected-jump quantum channel, a degradable channel modeling atomic decay, that approaches its quantum capacity by simulating a classical channel with erasures and bit-flips.

Contribution

It introduces a method to construct quantum codes for the detected-jump channel using classical codes, nearly reaching the channel's quantum capacity.

Findings

The classical capacity of the simulated channel provides a tight lower bound on the quantum capacity.

For small jump probabilities, the classical capacity approaches the quantum capacity.

The proposed coding scheme effectively approaches the quantum capacity of the detected-jump channel.

Abstract

The quantum channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known. Given the quantum capacity of a degradable channel, it remains challenging to find a practical coding scheme which approaches capacity. Here we discuss code designs for the detected-jump channel, a degradable channel with practical relevance describing the physics of spontaneous decay of atoms with detected photon emission. We show that this channel can be used to simulate a binary classical channel with both erasures and bit-flips. The capacity of the simulated classical channel gives a lower bound on the quantum capacity of the detected-jump channel. When the jump probability is small, it almost equals the quantum capacity. Hence using a classical capacity approaching code for the simulated classical channel yields a quantum code which approaches the quantum capacity of the detected-jump channel.