Measuring quantum entanglement without prior state reconstruction

TL;DR

This paper presents a method to measure quantum entanglement of two-qubit states directly, without full state reconstruction, using collective measurements on a small number of copies to estimate key parameters.

Contribution

It introduces a novel approach to directly measure entanglement measures like concurrence and negativity without prior state reconstruction.

Findings

Entanglement of formation can be measured without full state tomography.

Collective measurements on few copies suffice to estimate entanglement.

The method applies to both concurrence and negativity measures.

Abstract

It is shown that, despite strong nonlinearity, entanglement of formation of two-qubit state can be measured without prior state reconstruction. Collective measurements on small number of copies are provided that allow to determine quantum concurrence {\it via} estimation of only {\it four} parameters. It is also pointed out that another entanglement measure based on so called negativity can also be measured in similar way. The result is related to general problem: what kind of information can be extracted efficiently from unknown quantum state ?