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arXiv:2505.11303 · Physical Review Research

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

Jan Peřina, Nazarii Sudak, Artur Barasiński, Antonín Černoch

Published Nov 25, 2025• 0 citations
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Abstract

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.

DOI
10.1103/vd3h-4pts

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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.
Quantum universal invariants of general N -beam Gaussian fields are investigated from the point of view of fields' intensity moments. A method that uniquely links these invariants, including the global and marginal fields' purities, to intensity moments is suggested. Determination of these invariants identifies the Gaussian states including their quantum correlations. In particular, the Peres-Horodecki separability criterion is reformulated in terms of quantum universal invariants, and consequently in terms of experimental intensity moments, offering a practical tool for determining the entanglement or separability of these states. The approach is experimentally demonstrated by determining the invariants of noisy symmetric three-beam Gaussian states using photon-number resolved measurements. Furthermore, their entanglement properties are analyzed and characterized.
Quantum universal invariants of a Gaussian state's covariance matrix, which can be derived from intensity correlation moments, have been adopted to characterize the entanglement properties of Gaussian states via the positive partial transpose criterion, also known as the Peres-Horodecki separability criterion. Such intensity correlation moments enable the extraction of information about the covariance matrix without the need for a coherent local oscillator. Here, we experimentally detect the entanglement properties of multimode Gaussian states using high-order\,(up to sixth-order) intensity correlation moments. These multimode Gaussian states are prepared via spontaneous and cascaded parametric down-conversion pumped by a high-peak-energy pulsed laser. Their intensity correlation moments are measured using a pseudo-photon-number-resolving detector constructed through spatial multiplexing of 32 threshold superconducting nanowire single photon detectors. This method is successfully demonstrated for two-mode and three-mode Gaussian states and can be extended to NNN-mode Gaussian states with N>3N>3N>3.
Identification, and subsequent quantification of quantum correlations, is critical for understanding, controlling, and engineering quantum devices and processes. We derive and implement a general method to quantify various forms of quantum correlations using solely the experimental intensity moments up to the fourth order. This is possible as these moments allow for an exact determination of the global and marginal impurities of two-beam Gaussian fields. This leads to the determination of steering, tight lower and upper bounds for the negativity, and the Kullback-Leibler divergence used as a quantifier of state nonseparability. The principal squeezing variances are determined as well using the intensity moments. The approach is demonstrated on the experimental twin beams with increasing intensity and the squeezed super-Gaussian beams composed of photon pairs. Our method is readily applicable to multibeam Gaussian fields to characterize their quantum correlations.
Triple-photon states generated by three-mode spontaneous parametric down-conversion are the paradigm of unconditional non-Gaussian states, essential assets for quantum advantage. How to fully characterize their non-Gaussian entanglement remains however elusive. We propose here a set of sufficient and necessary conditions for separability of the broad family of spontaneously generated three-mode non-Gaussian states. We further derive state-of-the-art conditions for genuine tripartite non-Gaussian entanglement, the strongest class of entanglement. We apply our criteria to triple-photon states revealing that they are fully inseparable and genuinely entangled in moments of order 3n. Our results establish a systematic framework for characterizing the entanglement of triple-photon states and thus fostering their application in quantum information protocols.
We propose a direct measure of tripartite quantum entanglement in an arbitrary symmetric pure state of N correlated two-level atoms (qubits). We compute the third order moments of the collective pseudo-spin operators in terms of the individual atomic operators of the atoms in the assembly and find that all the bipartite quantum correlation terms among the atoms cancel out leaving only the all possible tripartite quantum correlation terms among them. We observe that the third order moments are made up of solely the tripartite quantum correlations among the atoms. This helps to extract out only the tripartite quantum correlations among the N atoms and propose a measure and quantification of these correlations. We also propose the necessary and sufficient condition for the presence of tripartite quantum entanglement in such multi-atomic systems. We conjecture the way of determining the third order moments of the pseudo-spin operators of the two-level atoms in the assembly, experimentally.