Experimental entropic uncertainty relations in dimensions three to five

TL;DR

This paper experimentally validates tight entropic uncertainty relations for high-dimensional quantum systems in dimensions 3 to 5, confirming theoretical bounds using frequency-bin measurements.

Contribution

It provides the first experimental verification of entropic uncertainty relations in dimensions three to five with mutually unbiased bases.

Findings

Experimental results match theoretical predictions.

The entropy sum bounds are never violated.

States saturate the bounds, minimizing uncertainty.

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.