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

TL;DR

This paper introduces new methods for self-testing maximally entangled states and single projective measurements in bipartite quantum systems using minimal measurement settings, extending previous results to higher dimensions.

Contribution

It demonstrates that all maximally entangled states can be self-tested with four binary measurements per party, and all single binary projective measurements with five binary measurements, regardless of dimension.

Findings

Maximally entangled states self-tested with four measurements per party

Single binary projective measurements self-tested with five measurements per party

Extension of self-testing to higher-dimensional states and measurements

Abstract

Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This paper considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and measurements of arbitrarily large dimension. The contributions are twofold. 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 Man\v{c}inska-Prakash-Schafhauser (2021), which applies to maximally entangled states of odd dimensions only. 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 quadruples of projections that add to a scalar multiple of the identity. Structure of irreducible representations, analysis of their spectral features and post-hoc self-testing are the primary methods for constructing the new self-tests with small number of inputs and outputs.