Characterization of measurement uncertainties using the correlations between local outcomes obtained from maximally entangled pairs
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.
Keywords
Cite
@article{arxiv.1502.06312,
title = {Characterization of measurement uncertainties using the correlations between local outcomes obtained from maximally entangled pairs},
author = {Shota Kino and Taiki Nii and Holger F. Hofmann},
journal= {arXiv preprint arXiv:1502.06312},
year = {2015}
}
Comments
10 pages, added comments on quasi-probabilities and quantum state reconstructions, final version for publication in Phys. Rev. A