{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T22:23:12Z","timestamp":1762035792306,"version":"build-2065373602"},"reference-count":0,"publisher":"Rinton Press","issue":"13&14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2014,10]]},"abstract":"<jats:p>We study the problem of distinguishing quantum states using local operations and classical communication (LOCC). A question of fundamental interest is whether there exist sets of $k \\leq d$ orthogonal maximally entangled states in $\\complex^{d}\\otimes\\complex^{d}$ that are not perfectly distinguishable by LOCC. A recent result by Yu, Duan, and Ying [Phys. Rev. Lett. 109 020506 (2012)] gives an affirmative answer for the case $k = d$. We give, for the first time, a proof that such sets of states indeed exist even in the case $k &lt; d$. Our result is constructive and holds for an even wider class of operations known as positive-partial-transpose measurements (PPT). The proof uses the characterization of the PPT-distinguishability problem as a semidefinite program.<\/jats:p>","DOI":"10.26421\/qic14.13-14-3","type":"journal-article","created":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:18:09Z","timestamp":1614557889000},"page":"1098-1106","source":"Crossref","is-referenced-by-count":8,"title":["Small sets of locally indistinguishable orthogonal maximally entangled states"],"prefix":"10.26421","volume":"14","author":[{"given":"Alessandro","family":"Cosentino","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Russo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10955","published-online":{"date-parts":[[2014,10]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:18:13Z","timestamp":1614557893000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC14.13-14-3.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10]]},"references-count":0,"journal-issue":{"issue":"13&14","published-online":{"date-parts":[[2014,10]]},"published-print":{"date-parts":[[2014,10]]}},"URL":"https:\/\/doi.org\/10.26421\/qic14.13-14-3","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"type":"print","value":"1533-7146"},{"type":"electronic","value":"1533-7146"}],"subject":[],"published":{"date-parts":[[2014,10]]}}}