Certifying dimension of quantum systems by sequential projective measurements

Adel Sohbi (1) , Damian Markham (2, 3) , Jaewan Kim (1) , Marco Túlio Quintino (4, 5)

1 KIAS - Korea Institute for Advanced Study
2 JFLI - Japanese French Laboratory for Informatics
3 QI - Information Quantique [LIP6]
4 University of Vienna [Vienna]
5 IQOQI - Institute for Quantum Optics and Quantum Information [Innsbruck]

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.

Domaines: Mathématiques [math]

Adel Sohbi, Damian Markham, Jaewan Kim, Marco Túlio Quintino. Certifying dimension of quantum systems by sequential projective measurements. Quantum, 2021, 5, pp.472. ⟨10.22331/q-2021-06-10-472⟩. ⟨hal-03270658⟩