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

Abstract

Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This talk considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and measurements of arbitrarily large dimension. 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 Fu (2022) on maximally entangled states of infinitely many even dimensions, and Mančinska-Prakash-Schafhauser (2021) on maximally entangled states of all odd dimensions. Secondly, it is shown that every single binary projective measurement can be self-tested with five binary measurements per party. A similar statement holds for self-testing of projective measurements with more than two outputs. These results are enabled by the representation theory of tuples of projections that add to a scalar multiple of the identity. Structure of their irreducible representations, analysis of their spectral features and post-hoc self-testing are the primary methods for constructing these self-tests with small number of inputs and outputs.

Zoom link: https://us06web.zoom.us/j/87431414089‍

Meeting ID: 874 3141 4089

Access code: nisq