Certifying dimension of quantum systems by sequential projective measurements

Adel Sohbi1, Damian Markham2,3, Jaewan Kim1, and Marco Túlio Quintino4,5

1School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
2LIP6, CNRS, Université Pierre et Marie Curie, Sorbonne Universités, 75005 Paris, France
3JFLI, CNRS, National Institute of Informatics, University of Tokyo, Tokyo, Japan
4Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
5Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

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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.

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[2] Giuseppe Vitagliano and Costantino Budroni, "Leggett-Garg macrorealism and temporal correlations", Physical Review A 107 4, 040101 (2023).

[3] Adel Sohbi, Ruben Ohana, Isabelle Zaquine, Eleni Diamanti, and Damian Markham, "Experimental approach to demonstrating contextuality for qudits", Physical Review A 103 6, 062220 (2021).

[4] Costantino Budroni, Giuseppe Vitagliano, and Mischa P. Woods, "Ticking-clock performance enhanced by nonclassical temporal correlations", Physical Review Research 3 3, 033051 (2021).

[5] Lucas B. Vieira and Costantino Budroni, "Temporal correlations in the simplest measurement sequences", Quantum 6, 623 (2022).

[6] Lorenzo Catani, Ricardo Faleiro, Pierre-Emmanuel Emeriau, Shane Mansfield, and Anna Pappa, "Connecting xor and xor * games", Physical Review A 109 1, 012427 (2024).

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