2018/06/30 by Spencer Breiner, Amir Kalev, Carl A. Miller · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.4204/eptcs.287.3
published as EPTCS 287, 2019, pp. 43-66 · In Proceedings QPL 2018, arXiv:1901.09476
arxiv created 2019/01/29 · arxiv updated 2019/01/30
Quantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in a three-party (rather than two-party) scenario, by showing that an arbitrary number of copies of the GHZ state can be self-tested. In order to handle the additional complexity of a three-party setting, we use a diagrammatic proof based on categorical quantum mechanics, rather than a typical symbolic proof. The diagrammatic approach allows for manipulations of the complicated tensor networks that arise in the proof, and gives a demonstration of the importance of picture-languages in quantum information.