[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"author":[{"last_name":"Jain","first_name":"Vishesh","full_name":"Jain, Vishesh"},{"last_name":"Kwan","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"},{"first_name":"Marcus","full_name":"Michelen, Marcus","last_name":"Michelen"}],"_id":"22813","arxiv":1,"supplementarymaterial":"no","date_updated":"2026-09-09T12:35:24Z","doi":"10.1007/s00220-026-05711-4","OA_place":"publisher","article_number":"214","language":[{"iso":"eng"}],"abstract":[{"text":"Consider a bipartite quantum system, where Alice and Bob jointly possess\r\na pure state |ψ\u0002. Using local quantum operations on their respective subsystems, and\r\nunlimited classical communication, Alice and Bob may be able to transform |ψ\u0002 into\r\nanother state |φ\u0002. Famously, Nielsen’s theorem [28] provides a necessary and sufficient\r\nalgebraic criterion for such a transformation to be possible (namely, the entanglement\r\nspectrum of |φ\u0002 should majorise the entanglement spectrum of |ψ\u0002). In the paper where\r\nNielsen proved this theorem, he conjectured that in the limit of large dimensionality, for\r\nalmost all pairs of states |ψ\u0002, |φ\u0002 (according to the natural unitary invariant measure) such\r\na transformation is not possible. That is to say, typical pairs of quantum states |ψ\u0002, |φ\u0002\r\nare entangled in fundamentally different ways, that cannot be converted to each other via\r\nlocal operations and classical communication.ViaNielsen’s theorem, this conjecture can\r\nbe equivalently stated as a conjecture about majorisation of spectra of random matrices\r\nfrom the so-called trace-normalised complex Wishart–Laguerre ensemble. Concretely,\r\nlet X and Y be independent n × m random matrices whose entries are i.i.d. standard\r\ncomplex Gaussians; then Nielsen’s conjecture says that the probability that the spectrum\r\nof XX†/ tr(XX†) majorises the spectrum of YY†/ tr(YY†) tends to zero as both n and\r\nm grow large. We prove this conjecture, and we also confirm some related predictions\r\nof Cunden et al. [12].","lang":"eng"}],"license":"https://creativecommons.org/licenses/by/4.0/","volume":407,"external_id":{"arxiv":["2406.03335"],"pmid":["42668663"]},"oa":1,"dataavailabilitystatement":"No datasets were used in this research.","publisher":"Springer","fulldoi":"https://doi.org/10.1007/s00220-026-05711-4","das_tickbox":"1","oa_version":"Published Version","day":"28","article_processing_charge":"Yes (via OA deal)","file_date_updated":"2026-09-09T12:32:53Z","corr_author":"1","article_type":"original","year":"2026","date_created":"2026-09-06T22:01:56Z","pmid":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","file":[{"file_size":463477,"date_created":"2026-09-09T12:32:53Z","access_level":"open_access","content_type":"application/pdf","date_updated":"2026-09-09T12:32:53Z","file_name":"2026_CommMathPhysics_Jain.pdf","relation":"main_file","checksum":"61c226b6314a88db25e864e4218d5de3","file_id":"22888","success":1,"creator":"dernst"}],"month":"08","department":[{"_id":"MaKw"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Vishesh Jain was partially supported by NSF CAREER award DMS-2237646. Matthew Kwan was supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. Marcus Michelen was supported in part by NSF grants DMS-2137623 and DMS-2246624.","ddc":["500"],"title":"Entangled states are typically incomparable","date_published":"2026-08-28T00:00:00Z","researchdata_availability":"no","PlanS_conform":"1","type":"journal_article","citation":{"short":"V. Jain, M.A. Kwan, M. Michelen, Communications in Mathematical Physics 407 (2026).","chicago":"Jain, Vishesh, Matthew Alan Kwan, and Marcus Michelen. “Entangled States Are Typically Incomparable.” <i>Communications in Mathematical Physics</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s00220-026-05711-4\">https://doi.org/10.1007/s00220-026-05711-4</a>.","ieee":"V. Jain, M. A. Kwan, and M. Michelen, “Entangled states are typically incomparable,” <i>Communications in Mathematical Physics</i>, vol. 407, no. 10. Springer, 2026.","mla":"Jain, Vishesh, et al. “Entangled States Are Typically Incomparable.” <i>Communications in Mathematical Physics</i>, vol. 407, no. 10, 214, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s00220-026-05711-4\">10.1007/s00220-026-05711-4</a>.","ista":"Jain V, Kwan MA, Michelen M. 2026. Entangled states are typically incomparable. Communications in Mathematical Physics. 407(10), 214.","apa":"Jain, V., Kwan, M. A., &#38; Michelen, M. (2026). Entangled states are typically incomparable. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-026-05711-4\">https://doi.org/10.1007/s00220-026-05711-4</a>","ama":"Jain V, Kwan MA, Michelen M. Entangled states are typically incomparable. <i>Communications in Mathematical Physics</i>. 2026;407(10). doi:<a href=\"https://doi.org/10.1007/s00220-026-05711-4\">10.1007/s00220-026-05711-4</a>"},"status":"public","OA_type":"hybrid","intvolume":"       407","has_accepted_license":"1","project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics","grant_number":"101076777"}],"publication":"Communications in Mathematical Physics","quality_controlled":"1","scopus_import":"1","issue":"10"}]