Generating Grid States From Schr\"odinger Cat States without Post-Selection

TL;DR

This paper presents a method to generate grid states from Schr"odinger cat states without post-selection by using measurement data post-processing, enhancing the practicality of the scheme.

Contribution

It introduces a post-processing technique that eliminates the need for post-selection in grid state generation from Schr"odinger cat states.

Findings

The method removes the need for post-selection in grid state generation.

Numerical demonstrations show the effectiveness of the approach.

Theoretical bounds on the asymptotic behavior of the breeding process.

Abstract

Grid (or comb) states are an interesting class of bosonic states introduced by Gottesman, Kitaev and Preskill to encode a qubit into an oscillator. A method to generate or `breed' a grid state from Schr\"odinger cat states using beam splitters and homodyne measurements is known, but this method requires post-selection. In this paper we show how post-processing of the measurement data can be used to entirely remove the need for post-selection, making the scheme much more viable. We bound the asymptotic behavior of the breeding procedure and demonstrate the efficacy of the method numerically.