Generalised All-Optical Cat Correction

TL;DR

This paper extends all-optical telecorrection protocols for higher-order cat codes, reducing iteration counts and enabling new transformations, with trade-offs in photon-number and complexity.

Contribution

It generalizes the telecorrection protocol to higher-order cat codes and introduces a probabilistic scheme for state deformation correction.

Findings

Higher-order cat codes achieve target fidelity with fewer iterations.

A third-order cat code reduces iterations by 70 times compared to first-order.

The scheme allows encoding new transformations and changing the code basis.

Abstract

We have generalised an all-optical telecorrection protocol for the higher orders of the cat code, and show that with these higher orders we can achieve target performance at substantially reduced iteration counts at the cost of a higher mean photon-number. We also introduce a probabilistic scheme for correcting deformation of the state, which highlights two interesting abilities of telecorrection: to encode new sets of transformations, and to change the basis of the code. We find that for a target channel fidelity of $99.9\%$ over a channel with $1\text{ dB}$ of loss, a third-order cat code requires $70$ times fewer telecorrection iterations than a first-order one, at a cost of a $3.6$-fold increase in mean photon-number.