The efficient witnessing and certification of entanglement is necessitated by its ubiquitous use in various aspects of quantum technologies. In the case of continuous-variable bipartite systems, the Shchukin-Vogel hierarchy gives necessary conditions for separability in terms of moments of the mode operators. In this work we derive mode-operator-based witnesses for continuous-variable bipartite entanglement relying on the interference of two states. Specifically, we show how one can access higher moments of the mode operators, crucial for detecting entanglement of non-Gaussian states, using a single beamsplitter with variable phase and photon-number-resolving detectors. We demonstrate that the use of an entangled state paired with a suitable reference state is sufficient to detect entanglement in, e.g., two-mode squeezed vacuum, NOON states, and mixed entangled cat states. We also take into account experimental noise, including photon loss and detection inefficiency, as well as finite measurement statistics.
Callus et al. (Thu,) studied this question.