Experimental entropic uncertainty relations in dimensions three to five

<jats:p> 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>d</a:mi> <a:mo>=</a:mo> <a:mn>3</a:mn> </a:mrow> </a:math> , 4, and 5 and consider from 2 to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>d</b:mi> <b:mo>+</b:mo> <b:mn>1</b:mn> </b:mrow> </b:math> mutually unbiased bases. The experiment is based on pulsed frequency bins measured with a multioutput 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. </jats:p>