Certifying dimension of quantum systems by sequential projective measurements

TL;DR

This paper develops improved methods for certifying the dimension of quantum systems through sequential projective measurements, enabling certification of systems with dimensions greater than two and three with high robustness.

Contribution

It refines existing techniques and demonstrates, for the first time, certification of quantum systems with dimension greater than three using sequential projective measurements.

Findings

Dimension greater than two can be certified with simpler scenarios.

Quantum systems with dimension greater than three can be certified for the first time in this setting.

Random measurements on pure qutrit states robustly certify quantum dimensions with high probability.

Abstract

This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random projective measurements on random pure qutrit states allows a robust certification of quantum dimensions with very high probability.