Self-testing in the compiled setting via tilted-CHSH inequalities

• URL: http://arxiv.org/abs/2406.04986v1
• Date: Fri, 7 Jun 2024 14:49:40 GMT
• Title: Self-testing in the compiled setting via tilted-CHSH inequalities
• Authors: Arthur Mehta, Connor Paddock, Lewis Wooltorton,
• Abstract summary: We formalize self-testing for compiled Bell scenarios. We prove the maximal quantum value is preserved under compilation for the family of tilted-CHSH inequalities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a Bell scenario, a classical verifier interacts with two non-communicating provers, producing a correlation. Certain correlations allow the verifier to certify, or self-test, the underlying quantum state and measurements. Notably, the family of tilted-CHSH inequalities has been used to self-test any two-qubit state. Self-tests underpin numerous device-independent protocols, however, a significant drawback of such applications is the non-communicating assumption. To address the non-communication assumption Kalai et al. (STOC'23) give a procedure which compiles a bipartite Bell scenario into a 2-round interaction between a verifier and a single computationally bounded prover. In this work, we formalize self-testing for compiled Bell scenarios. We prove the maximal quantum value is preserved under compilation for the family of tilted-CHSH inequalities, and that any maximal violation constitutes a compiled self-test. More specifically, we establish the existence of an efficient isometry recovering the state and measurements in the second round.

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