A mathematical foundation for self-testing: Lifting common assumptions
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915943787003904 |
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| author | Baptista, Pedro Chen, Ranyiliu Kaniewski, Jędrzej Lolck, David Rasmussen Mančinska, Laura Nielsen, Thor Gabelgaard Schmidt, Simon |
| author_facet | Baptista, Pedro Chen, Ranyiliu Kaniewski, Jędrzej Lolck, David Rasmussen Mančinska, Laura Nielsen, Thor Gabelgaard Schmidt, Simon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12662 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A mathematical foundation for self-testing: Lifting common assumptions Baptista, Pedro Chen, Ranyiliu Kaniewski, Jędrzej Lolck, David Rasmussen Mančinska, Laura Nielsen, Thor Gabelgaard Schmidt, Simon Quantum Physics 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. |
| title | A mathematical foundation for self-testing: Lifting common assumptions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2310.12662 |