Experimental implementation of a NMR entanglement witness

TL;DR

This paper experimentally tests an NMR-based entanglement witness for Bell-diagonal states, compares its efficiency with optimal witnesses and robustness measures, and demonstrates scenarios where witnesses fail but entanglement persists.

Contribution

It provides an experimental validation of a recently proposed NMR entanglement witness and introduces optimized witnesses with improved detection capabilities.

Findings

The proposed entanglement witness performs better than the initial one in certain conditions.

Both witnesses fail to detect entanglement after relaxation in some regions.

Generalized robustness can still detect entanglement when witnesses do not.

Abstract

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance.