Testing genuine tripartite quantum nonlocality with three two-level atoms in a driven cavity

Abstract

It is known that the violation of Svetlichny's inequality (SI), rather than the usual Mermin's inequality (MI), is a robust criterion to confirm the existence of genuine multipartite quantum nonlocality. In this paper, we propose a feasible approach to test SI with three two-level atoms (TLAs) dispersively coupled to a driven cavity. The proposal is based on the joint measurements of the states of three TLAs by probing the steady-state transmission spectra of the driven cavity: each peak marks one of the computational basis states and its relative height corresponds to the probability superposed in the detected three-TLA state. With these kinds of joint measurements, the correlation functions in SI can be directly calculated, and thus the SI can be efficiently tested for typical tripartite entanglement, i.e., genuine tripartite entanglement [e.g., Greenberger-Horne-Zeilinger (GHZ) and W states] and biseparable three-qubit entangled states (e.g., ${|\ensuremath{\chi}\ensuremath{\rangle}}_{12}{|\ensuremath{\xi}\ensuremath{\rangle}}_{3}$). Our numerical experiments show that the SI is violated only by three-qubit GHZ and W states, not by biseparable three-qubit entangled state ${|\ensuremath{\chi}\ensuremath{\rangle}}_{12}{|\ensuremath{\xi}\ensuremath{\rangle}}_{3}$, while the MI can still be violated by biseparable three-qubit entangled states. Thus the violation of SI can be regarded as a robust criterion for the existence of genuine tripartite entanglement.