{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T18:26:00Z","timestamp":1785522360776,"version":"3.56.0"},"reference-count":32,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T00:00:00Z","timestamp":1698105600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation, Singapore; and A*STAR","award":["CQT Bridging Grant"],"award-info":[{"award-number":["CQT Bridging Grant"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Bell&amp;apos;s theorem states that Local Hidden Variables (LHVs) cannot fully explain the statistics of measurements on some entangled quantum states. It is natural to ask how much supplementary classical communication would be needed to simulate them. We study two long-standing open questions in this field with neural network simulations and other tools. First, we present evidence that all projective measurements on partially entangled pure two-qubit states require only one bit of communication. We quantify the statistical distance between the exact quantum behaviour and the product of the trained network, or of a semianalytical model inspired by it. Second, while it is known on general grounds (and obvious) that one bit of communication cannot eventually reproduce all bipartite quantum correlation, explicit examples have proved evasive. Our search failed to find one for several bipartite Bell scenarios with up to 5 inputs and 4 outputs, highlighting the power of one bit of communication in reproducing quantum correlations.<\/jats:p>","DOI":"10.22331\/q-2023-10-24-1150","type":"journal-article","created":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T14:42:47Z","timestamp":1698158567000},"page":"1150","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Neural Network Approach to the Simulation of Entangled States with One Bit of Communication"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5003-6242","authenticated-orcid":false,"given":"Peter","family":"Sidajaya","sequence":"first","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aloysius Dewen","family":"Lim","sequence":"additional","affiliation":[{"name":"Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8354-8343","authenticated-orcid":false,"given":"Baichu","family":"Yu","sequence":"additional","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543"},{"name":"Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Nanshan District, Shenzhen, 518055, China"},{"name":"International Quantum Academy (SIQA), Shenzhen 518048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5594-5616","authenticated-orcid":false,"given":"Valerio","family":"Scarani","sequence":"additional","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543"},{"name":"Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,10,24]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Albert Einstein, Boris Podolsky, and Nathan Rosen. 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