A mathematical foundation for self-testing: Lifting common assumptions

• URL: http://arxiv.org/abs/2310.12662v1
• Date: Thu, 19 Oct 2023 11:41:31 GMT
• Title: A mathematical foundation for self-testing: Lifting common assumptions
• Authors: Pedro Baptista, Ranyiliu Chen, J\k{e}drzej Kaniewski, David Rasmussen Lolck, Laura Man\v{c}inska, Thor Gabelgaard Nielsen, Simon Schmidt
• Abstract summary: We study the phenomenon of self-testing from the first principles, aiming to place this versatile concept on a rigorous mathematical footing. We identify a quantum correlation which is a self-test only if certain assumptions are made. Remarkably, this is also the first example of a correlation that cannot be implemented using projective measurements on a bipartite state of full Schmidt rank.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work we study the phenomenon of self-testing from the first principles, aiming to place this versatile concept on a rigorous mathematical footing. Self-testing allows a classical verifier to infer a quantum mechanical description of untrusted quantum devices that she interacts with in a black-box manner. Somewhat contrary to the black-box paradigm, existing self-testing results tend to presuppose conditions that constrain the operation of the untrusted devices. A common assumption is that these devices perform a projective measurement of a pure quantum state. Naturally, in the absence of any prior knowledge it would be appropriate to model these devices as measuring a mixed state using POVM measurements, since the purifying/dilating spaces could be held by the environment or an adversary. We prove a general theorem allowing to remove these assumptions, thereby promoting most existing self-testing results to their assumption-free variants. On the other hand, we pin-point situations where assumptions cannot be lifted without loss of generality. As a key (counter)example we identify a quantum correlation which is a self-test only if certain assumptions are made. Remarkably, this is also the first example of a correlation that cannot be implemented using projective measurements on a bipartite state of full Schmidt rank. Finally, we compare existing self-testing definitions, establishing many equivalences as well as identifying subtle differences.

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