Quasiprobabilities for multipartite quantum correlations of light

Regular quasiprobabilities are introduced for the aim of characterizing quantum correlations of multimode radiation fields. Negativities of these quantum-correlation quasiprobabilities are necessary and sufficient for any quantum correlation encoded in the multimode Glauber-Sudarshan $P$ function. The strength of the method is demonstrated for a two-mode, phase-randomized, squeezed-vacuum state. It has no entanglement, no quantum discord, a positive Wigner function, and a classical reduced single-mode representation. Our method clearly visualizes the quantum correlations of this state.

Figure 1

Experimental setup for the generation of a phase-randomized, two-mode, squeezed vacuum. A 50:50 beam splitter combines squeezed-vacuum states, which are squeezed in orthogonal quadratures. One of the output channels is fully phase randomized, $\delta \phi =2\pi$.

Figure 2

The Wigner function is shown for a fully phase-randomized, two-mode, squeezed-vacuum state, with $p=0.8$. It is non-negative in the full two-mode phase space.

Figure 3

The regularized quasiprobability $P_{\mathrm{QC}}$ is shown for a fully phase-randomized, two-mode, squeezed-vacuum state for $p=0.8$ and $w=1.5$. Clear negativities visualize the nonclassical correlations of the state.