Quantum error correction against photon loss using multi-component cat states

TL;DR

This paper develops a generalized quantum error correction code using multi-component cat states to protect against photon loss, extending existing codes and enabling logical qubit and qudit protection in quantum communication.

Contribution

It introduces a systematic code construction for photon loss correction using multi-component cat states, extending previous codes to higher loss numbers and logical qudits.

Findings

Encoded qubits show cyclic behaviour under photon loss channels.

The code can correct half of the photon losses in the cycle.

Application demonstrated in a one-way quantum communication scheme.

Abstract

We analyse a generalised quantum error correction code against photon loss where a logical qubit is encoded into a subspace of a single oscillator mode that is spanned by distinct multi-component cat states (coherent-state superpositions). We present a systematic code construction that includes the extension of an existing one-photon-loss code to higher numbers of losses. When subject to a photon loss (amplitude damping) channel, the encoded qubits are shown to exhibit a cyclic behaviour where the code and error spaces each correspond to certain multiples of losses, half of which can be corrected. As another generalisation we also discuss how to protect logical qudits against photon losses, and as an application we consider a one-way quantum communication scheme, in which the encoded qubits are periodically recovered while the coherent-state amplitudes are restored as well at regular intervals.