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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 243, Functional Analysis Seminar
Dr. Jitendra Prakash
University of New Orleans
Constant-sized robust self-tests for states and measurements of unbounded dimension
Abstract:
In quantum information, robust self-test is a desirable property for quantum devices through which one can certify the quantum-mechanical promises of the device based solely on classical statistics. We consider quantum 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 xl. 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 dimension as well as 2-outcome projective measurements of arbitrarily high rank.
Hosts: David Jekel and Priyanga Ganesan
January 31, 2023
11:00 AM
Zoom (email djekel@ucsd.edu for Zoom info)
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