Self-testing in prepare-and-measure scenarios and a robust version of Wigner's theorem

Abstract

We consider communication scenarios where one party sends quantum states of known dimensionality $D$, prepared with an untrusted apparatus, to another, distant party, who probes them with uncharacterized measurement devices. We prove that, for any ensemble of reference pure quantum states, there exists one such prepare-and-measure scenario and a linear functional $W$ on its observed measurement probabilities, such that $W$ can only be maximized if the preparations coincide with the reference states, modulo a unitary or an anti-unitary transformation. In other words, prepare-and-measure scenarios allow one to "self-test" arbitrary ensembles of pure quantum states. Arbitrary extreme $D$-dimensional quantum measurements, or sets thereof, can be similarly self-tested. Our results rely on a robust generalization of Wigner's theorem, a well-known result in particle physics that characterizes physical symmetries.

arXiv commentv3: Close to published version. v4: Additional typos fixed

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• Memory attacks in network nonlocality and self-testing
• Absolute dimensionality of quantum ensembles
• Global restrictions under local state discrimination
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Classical certification of quantum gates under the dimension assumption
• Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints
• Semi-device-independent self-testing of unitary operations
• Certifying asymmetry in the configuration of three qubits
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements
• Quantum description of reality is epistemically incomplete