Assessing non-Gaussian quantum state conversion with the stellar rank

• URL: http://arxiv.org/abs/2410.23721v3
• Date: Mon, 25 Nov 2024 01:59:05 GMT
• Title: Assessing non-Gaussian quantum state conversion with the stellar rank
• Authors: Oliver Hahn, Giulia Ferrini, Alessandro Ferraro, Ulysse Chabaud,
• Abstract summary: State conversion is a fundamental task in quantum information processing. We introduce a framework for assessing approximate Gaussian state conversion. We derive bounds for Gaussian state conversion under both approximate and probabilistic conditions.
• Score: 41.94295877935867
• License:
• Abstract: State conversion is a fundamental task in quantum information processing. Quantum resource theories allow to analyze and bound 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 under both approximate and probabilistic conditions, yielding new no-go results for non-Gaussian state preparation and enabling a reliable assessment of the performance of generic Gaussian conversion protocols.

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