Witnesses of genuine multipartite entanglement and nonlocal measurement backaction for Raman-scattering quantum systems

Entanglement between remote quantum mechanical systems enables a range of quantum information tasks in communication, computation and distributed sensing. Large numbers of entangled subsystems also require experimentally accessible and practically feasible methods of verifying the genuine, i.e., simultaneous, entanglement of all subsystems. We have derived a class of entanglement witnesses suitable for $W$-states, which are states where a single excitation is coherently distributed across subsystems initially in their ground state or a state with low thermal occupation, e.g., via detection of a Raman-scattered photon. The entanglement is witnessed through violation of an inequality involving number statistics, which can be measured via detection of subsequent Raman-scattered photons. Unlike conventional, partially tomographic, witnesses, our method is experimentally accessible for both multipartite and continuous variable systems. The thermal robustness of the method is quantified by the initial thermal occupations for which violation occurs. As an alternative approach, we have derived an inequality which tests the nonlocal, or quantum coherent, nature of the photon measurement backaction which produces the $W$-state. Violation of this alternative inequality implies the entanglement of the resulting state given the assumption of a separable initial state, under less stringent thermal constraints than the general entanglement witness. Our results are applicable to all Raman-scattering systems which can exhibit sufficient degrees of quantum indistinguishability.