Constant-sized robust self-tests for states and measurements of unbounded dimension

• URL: http://arxiv.org/abs/2103.01729v1
• Date: Tue, 2 Mar 2021 14:02:17 GMT
• Title: Constant-sized robust self-tests for states and measurements of unbounded dimension
• Authors: Laura Man\v{c}inska, Jitendra Prakash, Christopher Schafhauser
• Abstract summary: We show that correlations $p_n,x$ robustly self-test the underlying states and measurements. We are the first to exhibit a constant-sized self-test for measurements of unbounded dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider correlations, $p_{n,x}$, arising from measuring a maximally entangled state using $n$ measurements with two outcomes each, constructed from $n$ projections that add up to $xI$. We show that the correlations $p_{n,x}$ robustly self-test the underlying states and measurements. To achieve this, we lift the group-theoretic Gowers-Hatami based approach for proving robust self-tests to a more natural algebraic framework. A key step is to obtain an analogue of the Gowers-Hatami theorem allowing to perturb an "approximate" representation of the relevant algebra to an exact one. For $n=4$, the correlations $p_{n,x}$ self-test the maximally entangled state of every odd dimension as well as 2-outcome projective measurements of arbitrarily high rank. The only other family of constant-sized self-tests for strategies of unbounded dimension is due to Fu (QIP 2020) who presents such self-tests for an infinite family of maximally entangled states with even local dimension. Therefore, we are the first to exhibit a constant-sized self-test for measurements of unbounded dimension as well as all maximally entangled states with odd local dimension.

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