Certifying sets of quantum observables with any full-rank state

Abstract

We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this ``certification with any full-rank state'' (CFR) is possible for any quantum system of finite dimension $d\ge 3$ and is robust and experimentally useful in dimensions 3 and 4. In addition, we prove that complete Kochen-Specker sets can be Bell self-tested if and only if they enable CFR. This establishes a fundamental connection between these two methods of certification, shows that both methods can be combined in the same experiment, and opens new possibilities for certifying quantum devices.

arXiv comment5+18 pages, 0+2 figures, 1+6 tables

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• A computational test of quantum contextuality, and even simpler proofs of quantumness
• Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
• Contextuality of Quantum Error-Correcting Codes
• Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies
• Supersinglets can be self-tested with perfect quantum strategies
• Convexity of noncontextual wirings and how they order the set of correlations
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements