{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T03:29:39Z","timestamp":1767842979866,"version":"3.49.0"},"reference-count":68,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We analytically and numerically show that the Hillery-Zubairy\u2019s entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.<\/jats:p>","DOI":"10.3390\/e23050624","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T12:19:57Z","timestamp":1621253997000},"page":"624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators"],"prefix":"10.3390","volume":"23","author":[{"given":"Yoshitaka","family":"Inui","sequence":"first","affiliation":[{"name":"Physics and Informatics Laboratories, NTT Research Inc., 940 Stewart Dr, Sunnyvale, CA 94085, USA"}]},{"given":"Yoshihisa","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"Physics and Informatics Laboratories, NTT Research Inc., 940 Stewart Dr, Sunnyvale, CA 94085, USA"},{"name":"E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"063853","DOI":"10.1103\/PhysRevA.88.063853","article-title":"Coherent Ising machine based on degenerate optical parametric oscillators","volume":"88","author":"Wang","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1038\/nphoton.2014.249","article-title":"Network of time-multiplexed optical parametric oscillators as a coherent Ising machine","volume":"8","author":"Marandi","year":"2014","journal-title":"Nat. Photon."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"043821","DOI":"10.1103\/PhysRevA.92.043821","article-title":"Quantum correlation in degenerate optical parametric oscillators with mutual injections","volume":"92","author":"Takata","year":"2015","journal-title":"Phys. Rev. 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