Witnessing genuine multipartite entanglement in phase space with controlled Gaussian unitaries

Abstract

Many existing genuine multipartite entanglement (GME) witnesses for continuous-variable (CV) quantum systems typically rely on quadrature measurements, which is challenging to implement in platforms where the CV degrees of freedom can be indirectly accessed only through qubit readouts. In this work, we propose methods to implement GME witnesses through phase-space measurements in state-of-the-art experimental platforms, leveraging controlled Gaussian unitaries readily available in qubit-CV architectures. Based on two theoretical results showing that sufficient Wigner negativity can certify GME, we present five concrete implementation schemes using controlled parity, displacement, and beamsplitter operations. Our witnesses can detect paradigmatic GME states like the Dicke and multipartite $N00N$ states, which include the W states as a special case, and GHZ-type entangled cat states. We analyze the performance of these witnesses under realistic noise conditions and finite measurement resolution, showing their robustness to experimental imperfections. Crucially, our implementations require exponentially fewer measurement settings than full tomography, with one scheme requiring only a single measurement on auxiliary modes. The methods are readily applicable to circuit/cavity quantum electrodynamics, circuit quantum acoustodynamics, as well as trapped ions and atoms systems, where such dichotomic phase-space measurements are already routinely performed as native readouts.