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Constant-sized self-tests for maximally entangled states and single local projective measurements
Journal article   Open access   Peer reviewed

Constant-sized self-tests for maximally entangled states and single local projective measurements

Jurij Volcic
Quantum (Vienna, Austria), v 8, 1292
21 Mar 2024
DOI: https://doi.org/10.22331/q-2024-03-21-1292
url
https://doi.org/10.22331/q-2024-03-21-1292View
Published, Version of Record (VoR)CC BY V4.0,  Open

Abstract

Physics, Multidisciplinary Quantum Science & Technology Science & Technology Physical Sciences Physics
Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This paper considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and measurements of arbitrarily large dimension. The contributions are twofold. Firstly, it is shown that every maximally entangled state can be self-tested with four binary measurements per party. This result extends the earlier work of Man.cinska-Prakash-Schafhauser (2021), which applies to maximally entangled states of odd dimensions only. Secondly, it is shown that every single local binary projective measurement can be self-tested with five binary measurements per party. A similar statement holds for self-testing of local projective measurements with more than two outputs. These results are enabled by the representation theory of quadruples of projections that add to a scalar multiple of the identity. Structure of irreducible representations, analysis of their spectral features and post-hoc self-testing are the primary methods for constructing the new self-tests with small number of inputs and outputs.

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Physics, Multidisciplinary
Quantum Science & Technology
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