##### 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:

*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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