{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T00:54:30Z","timestamp":1776732870105,"version":"3.51.2"},"reference-count":54,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T00:00:00Z","timestamp":1738627200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"A set of pure quantum states is said to be antidistinguishable if upon sampling one at random, there exists a measurement to perfectly determine some state that was not sampled. We show that antidistinguishability of a set of n<\/mml:mi><\/mml:math> pure states is equivalent to a property of its Gram matrix called (<\/mml:mo>n<\/mml:mi>&#x2212;<\/mml:mo>1<\/mml:mn>)<\/mml:mo><\/mml:math>-incoherence, thus establishing a connection with quantum resource theories that lets us apply a wide variety of new tools to antidistinguishability. As a particular application of our result, we present an explicit formula (not involving any semidefinite programming) that determines whether or not a set with a circulant Gram matrix is antidistinguishable. We also show that if all inner products are smaller than (<\/mml:mo>n<\/mml:mi>&#x2212;<\/mml:mo>2<\/mml:mn>)<\/mml:mo>\/<\/mml:mo><\/mml:mrow>(<\/mml:mo>2<\/mml:mn>n<\/mml:mi>&#x2212;<\/mml:mo>2<\/mml:mn>)<\/mml:mo><\/mml:msqrt><\/mml:math> then the set must be antidistinguishable, and we show that this bound is tight when n<\/mml:mi>&#x2264;<\/mml:mo>4<\/mml:mn><\/mml:math>. We also give a simpler proof that if all the inner products are strictly larger than (<\/mml:mo>n<\/mml:mi>&#x2212;<\/mml:mo>2<\/mml:mn>)<\/mml:mo>\/<\/mml:mo><\/mml:mrow>(<\/mml:mo>n<\/mml:mi>&#x2212;<\/mml:mo>1<\/mml:mn>)<\/mml:mo><\/mml:math>, then the set cannot be antidistinguishable, and we show that this bound is tight for all n<\/mml:mi><\/mml:math>.<\/jats:p>","DOI":"10.22331\/q-2025-02-04-1622","type":"journal-article","created":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T17:08:34Z","timestamp":1738688914000},"page":"1622","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Tight bounds for antidistinguishability and circulant sets of pure quantum states"],"prefix":"10.22331","volume":"9","author":[{"given":"Nathaniel","family":"Johnston","sequence":"first","affiliation":[{"name":"Department of Mathematics & Computer Science, Mount Allison University, Sackville, NB, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Russo","sequence":"additional","affiliation":[{"name":"Unitary Fund"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jamie","family":"Sikora","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,2,4]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Carlton M. 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