Quantum correlations in three-beam symmetric Gaussian states accessed via photon-number-resolving detection and quantum universal invariants

Quantum correlations of symmetric three-beam Gaussian states are analyzed using their quantum universal invariants. These invariants, one-, two-, and three-beam purities, are expressed in terms of the beams’ intensity moments up to sixth order. The three-beam symmetric Gaussian states with varying amounts of the noise are experimentally generated using entangled photon pairs from down-conversion, their invariants are determined, and their quantum correlations are quantified. The coexistence of bipartite and tripartite entanglement and genuine tripartite entanglement is observed in these states that resemble the noisy GHZ/W states.