Entanglement witnesses with variable number of local measurements

TL;DR

This paper introduces entanglement identifiers that require only partial measurement data to confirm entanglement, making experimental detection more feasible and efficient.

Contribution

It proposes a new class of entanglement identifiers based on sums of non-negative functions of correlations, which can confirm entanglement with fewer measurements.

Findings

Identifiers can detect entanglement with partial measurement data

They are based on sums of correlation functions, mainly squares

Examples demonstrate their effectiveness and advantages

Abstract

We present a class of entanglement identifiers which has the following experimentally friendly feature: once the expectation value of the identifier exceeds some definite limit, we can conclude the state is entangled, even if not all measurements defining the identifier have been performed. These identifiers are in the form of sums of non-negative functions of correlations in a quantum state, mostly squares of correlations, and we illustrate their use and strengths on various examples.