Generation of Non-Gaussian States in the Squeezed State Entanglement Scheme

TL;DR

This paper presents a general method to generate and analyze non-Gaussian quantum states using an entangled photon measurement scheme, enabling tailored state creation for quantum error correction with high fidelity.

Contribution

The authors derive explicit, general expressions for the output states' wave and Wigner functions, allowing comprehensive analysis and targeted state generation in the scheme.

Findings

High-fidelity Schrödinger cat states with 18% probability

Explicit formulas enable state optimization for quantum error correction

Analysis of non-Gaussianity depending on scheme parameters

Abstract

The paper considers the possibility of generating different non-Gaussian states using the entangled state photon measurement scheme. In the paper, we have proposed a way to explicitly find the wave function and the Wigner function of the output state of this scheme. Moreover, the solutions found are not restricted to any particular case, but have maximum generality (depend on the number of measured photons and on all parameters of the scheme). Such a notation allowed us to carry out a complete analysis of the output states, depending on the scheme parameters. Using explicit expressions, we have analyzed the magnitude of non-Gaussianity of the output states, and we have revealed which particular states can be obtained in the proposed scheme. We have considered in detail a particular case of measurement (single photon measurement) and have shown that using explicit expressions for the output state wave function one can find scheme parameters to obtain states suitable for quantum error correction codes with a large fidelity value and high probability. The Schrodinger cat state with amplitude $\alpha=2$ can be obtained with fidelity $F \approx 0.88$ and probability 18 percent, and the squeezed Schrodinger cat state ($\alpha=0.5$, $R=1$) with fidelity $F \approx 0.98$ and probability 22 percent.