Constantsized robust selftests for states and measurements of unbounded dimension
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 selftest the underlying states and measurements. To achieve this, we lift the grouptheoretic GowersHatami based approach for proving robust selftests to a more natural algebraic framework. A key step is to obtain an analogue of the GowersHatami theorem allowing to perturb an "approximate" representation of the relevant algebra to an exact one. For $n=4$, the correlations $p_{n,x}$ selftest the maximally entangled state of every odd dimension as well as 2outcome projective measurements of arbitrarily high rank. The only other family of constantsized selftests for strategies of unbounded dimension is due to Fu (QIP 2020) who presents such selftests for an infinite family of maximally entangled states with even local dimension. Therefore, we are the first to exhibit a constantsized selftest for measurements of unbounded dimension as well as all maximally entangled states with odd local dimension.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 DOI:
 10.48550/arXiv.2103.01729
 arXiv:
 arXiv:2103.01729
 Bibcode:
 2021arXiv210301729M
 Keywords:

 Quantum Physics;
 Mathematics  Operator Algebras;
 81P40 (Primary) 81P40;
 47C15 (Secondary)
 EPrint:
 38 pages