Directly comparing entanglement-enhancing non-Gaussian operations

Single-photon-level non-Gaussian operations-photon addition, photon subtraction, and their coherent superposition-are powerful tools with which to increase entanglement in continuous-variable optical states. Although such operations are typically not deterministic, there may be other advantages such as noiseless manipulation. Therefore, to fully account for the efficacy of a particular non-Gaussian operation in a practical scenario, we develop figures of merit which trade off the advantages of such protocols against their success probability. Specifically, we define 'entanglement enhancement rate' as the increase in entanglement per trial of a generic non-Gaussian operation on a two-mode squeezed vacuum (TMSV) state. We consider states generated by photon-subtraction, photon-addition and a coherent superposition of subtraction and addition. We compare each strategy when applied to one or both modes of a TMSV state, and also in the presence of channel losses prior to the operation. In many cases, additional properties are analytically calculable, including excess noise arising from the operation and the fidelity of the resulting states to particular Gaussian and non-Gaussian states. Finally, by incorporating loss, we derive optimal interaction parameters for each non-Gaussian operation which maximize the effectiveness of the particular protocol under investigation.