An operator system approach to self-testing

• URL: http://arxiv.org/abs/2506.17980v1
• Date: Sun, 22 Jun 2025 10:38:58 GMT
• Title: An operator system approach to self-testing
• Authors: Jason Crann, Ivan G. Todorov, Lyudmila Turowska,
• Abstract summary: We propose a definition of a local isometry between bipartite quantum systems in the commuting operator model.<n>We show that self-tests are in the general case always abstract self-tests and that, in some cases, the converse is also true.<n>We apply our framework in a variety of instances, including to correlations with quantum inputs and outputs, quantum commuting correlations for the CHSH game, synchronous correlations, contextuality scenarios, quantum colourings and Schur quantum channels.
• Score: 0.27309692684728604
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a general framework for self-testing, in which bipartite correlations are described by states on the commuting tensor product of a pair of operator systems. We propose a definition of a local isometry between bipartite quantum systems in the commuting operator model, and define self-testing and abstract self-testing in the latter generality. We show that self-tests are in the general case always abstract self-tests and that, in some cases, the converse is also true. We apply our framework in a variety of instances, including to correlations with quantum inputs and outputs, quantum commuting correlations for the CHSH game, synchronous correlations, contextuality scenarios, quantum colourings and Schur quantum channels.

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