Bell nonlocality and fully-entangled fraction measured in an entanglement-swapping device without quantum state tomography

TL;DR

This paper presents an efficient experimental method using entanglement swapping to measure Bell nonlocality and fully-entangled fraction of two-qubit states without full quantum state tomography, simplifying entanglement assessment.

Contribution

The authors introduce a novel entanglement swapping-based procedure to directly measure nonlocality and entanglement witnesses, reducing measurement complexity compared to traditional methods.

Findings

Successfully measured Bell nonlocality and entangled fraction without full tomography.

Estimated negativity of Werner states using the proposed method.

Demonstrated potential application in quantum communication protocols.

Abstract

We demonstrate an efficient experimental procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully-entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. Our method requires neither full quantum state tomography of 15 parameters nor continuous scanning of the measurement bases used by two parties in the usual CHSH inequality tests with four measurements in each optimization step. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully-entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measured these witnesses and estimated the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping.