Characterization of measurement uncertainties using the correlations between local outcomes obtained from maximally entangled pairs

TL;DR

This paper demonstrates that correlations between measurement errors of non-commuting observables can be directly observed in entangled quantum systems, revealing the role of non-commutativity and imaginary correlations in quantum measurement statistics.

Contribution

It introduces a method to characterize measurement error correlations using entangled pairs, highlighting the necessity of imaginary correlations for non-commuting observables in quantum theory.

Findings

Measurement error correlations are observable in entangled systems.

Quantum theory predicts imaginary correlations between non-commuting observables.

These correlations are linked to the operator product XY=iZ.

Abstract

Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However, a complete characterization of measurement errors must include the correlations between the errors of the two observables. Here, we show that these correlations appear in the experimentally observable measurement statistics obtained by performing the joint measurement on maximally entangled pairs. For two-level systems, the results indicate that quantum theory requires imaginary correlations between the measurement errors of X and Y since these correlations are represented by the operator product XY=iZ in the measurement operators. Our analysis thus reveals a directly observable consequence of non-commutativity in the statistics of quantum measurements.