Experimental entropic uncertainty relations in dimensions three to five

• URL: http://arxiv.org/abs/2507.05025v1
• Date: Mon, 07 Jul 2025 14:08:38 GMT
• Title: Experimental entropic uncertainty relations in dimensions three to five
• Abstract summary: We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions.<n>Our results fit the theoretical predictions: the bound on the sum of the entropies is never violated and is saturated by the states that minimize the uncertainty relations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide experimental validation of tight entropic uncertainty relations for the Shannon entropies of observables with mutually unbiased eigenstates in high dimensions. In particular, we address the cases of dimensions $d = 3$, $4$ and $5$ and consider from $2$ to $d+1$ mutually unbiased bases. The experiment is based on pulsed frequency bins measured with a multi-output quantum pulse gate, which can perform projective measurements on a complete high-dimensional basis in the time-frequency domain. Our results fit the theoretical predictions: the bound on the sum of the entropies is never violated and is saturated by the states that minimize the uncertainty relations.

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