Entanglement detection with imprecise measurements

TL;DR

This paper explores how measurement inaccuracies affect entanglement detection, providing methods to correct entanglement witnesses and ensuring reliable detection despite device imperfections.

Contribution

It introduces an operational inaccuracy measure, derives tight corrections for entanglement witnesses, and develops semidefinite programming techniques for bounding correlations under measurement errors.

Findings

Small measurement inaccuracies can significantly affect entanglement detection.

Methods to compute corrections for entanglement witnesses based on inaccuracy levels.

Semidefinite programming bounds correlations in the presence of measurement imprecision.

Abstract

We investigate entanglement detection when the local measurements only nearly correspond to those intended. This corresponds to a scenario in which measurement devices are not perfectly controlled, but nevertheless operate with bounded inaccuracy. We formalise this through an operational notion of inaccuracy that can be estimated directly in the lab. To demonstrate the relevance of this approach, we show that small magnitudes of inaccuracy can significantly compromise several renowned entanglement witnesses. For two arbitrary-dimensional systems, we show how to compute tight corrections to a family of standard entanglement witnesses due to any given level of measurement inaccuracy. We also develop semidefinite programming methods to bound correlations in these scenarios.