Experimental test of an entropic measurement uncertainty relation for arbitrary qubit observables

TL;DR

This paper experimentally tests a tight entropic measurement uncertainty relation for neutron spin-1/2 qubits, demonstrating the tradeoff between measurement noises for arbitrary observables and confirming theoretical predictions about optimal bounds.

Contribution

It provides the first experimental verification of a general entropic uncertainty relation for arbitrary qubit observables, including the role of POVMs.

Findings

Optimal bounds of measurement noise tradeoff are experimentally obtained.

Projective measurements reach the bounds for some observables.

General quantum measurements can saturate the tradeoff in other cases.

Abstract

A tight information-theoretic measurement uncertainty relation is experimentally tested with neutron spin-1/2 qubits. The noise associated to the measurement of an observable is defined via conditional Shannon entropies and a tradeoff relation between the noises for two arbitrary spin observables is demonstrated. The optimal bound of this tradeoff is experimentally obtained for various non-commuting spin observables. For some of these observables this lower bound can be reached with projective measurements, but we observe that, in other cases, the tradeoff is only saturated by general quantum measurements (i.e., positive-operator valued measures), as predicted theoretically.