Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant

Abstract

We address the problem of testing the quantumness of two-dimensional systems in the prepare-and-measure (PM) scenario, using a large number of preparations and a large number of measurement settings, with binary outcome measurements. In this scenario, we introduce constants, which we relate to the Grothendieck constant of order 3. We associate them with the white noise resistance of the prepared qubits and to the critical detection efficiency of the measurements performed. Large-scale numerical tools are used to bound the constants. This allows us to obtain new bounds on the minimum detection efficiency that a setup with 70 preparations and 70 measurement settings can tolerate.

16 pages, 1 figure

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• Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
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• Connecting XOR and XOR* games
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Classical bounds on two-outcome bipartite Bell expressions and linear prepare-and-measure witnesses: Efficient computation in parallel environments such as graphics processing units