Assessing non-Gaussian quantum state conversion with the stellar rank

TL;DR

This paper introduces an extended stellar rank measure to evaluate approximate non-Gaussian state conversion in quantum systems, providing bounds and an open-source tool for practical assessment.

Contribution

It extends the stellar rank to approximate conversions, deriving bounds and offering a Python library for assessing Gaussian state conversion performance.

Findings

Derived bounds for approximate Gaussian state conversion and distillation.

Established no-go results for non-Gaussian state preparation.

Provided an open-source Python library for stellar rank computations.

Abstract

State conversion is a fundamental task in quantum information processing. Quantum resource theories allow for analyzing and bounding conversions that use restricted sets of operations. In the context of continuous-variable systems, state conversions restricted to Gaussian operations are crucial for both fundamental and practical reasons, particularly in state preparation and quantum computing with bosonic codes. However, previous analysis did not consider the relevant case of approximate state conversion. In this work, we introduce a framework for assessing approximate Gaussian state conversion by extending the stellar rank to the approximate stellar rank, which serves as an operational measure of non-Gaussianity. We derive bounds for Gaussian state conversion and distillation under approximate and probabilistic conditions, yielding new no-go results for non-Gaussian state preparation and enabling a reliable assessment of the performance of Gaussian conversion protocols. We also provide an open-source Python library to compute stellar-rank-related quantities and to assess Gaussian conversion.