Document Zbl 1402.81063

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Process.</a> <a href="/?q=in%3A377390" title="Articles in this Issue">17, No. 2, Paper No. 29, 12 p. (2018)</a>. </div> <div class="abstract">Summary: We investigate the distinguishability of orthogonal generalized Bell states (GBSs) in $d\otimes d$ system by local operations and classical communication (LOCC), where $d$ is a prime. We show that $|S|$ is no more than $d+1$ for any $l$ GBSs, i.e., $|S|\leq d+1$, where $S$ is maximal set which is composed of pairwise noncommuting pairs in ${\varDelta } U$. If $|S|\leq d$, then the $l$ GBSs can be distinguished by LOCC according to our main Theorem. Compared with the results of <span class="zbmathjax-textit">H. Fan</span> [“Distinguishability and indistinguishability by local operations and classical communication”, Phys. Rev. Lett. 92, No. 17, Article ID 177905, 4 p. (2004; <a href="https://doi.org/10.1103/PhysRevLett.92.177905">doi:10.1103/PhysRevLett.92.177905</a>)] and <span class="zbmathjax-textit">G. Tian</span> et al. [“Local discrimination of qudit lattice states via commutativity”, Phys. Rev. A (3) 92, No. 4, Article ID 042320, 4 p. (2015; <a href="https://doi.org/10.1103/PhysRevA.92.042320">doi:10.1103/PhysRevA.92.042320</a>)], our result is more general. It can determine local distinguishability of $l (> k)$ GBSs, where $k$ is the number of GBSs in Fan’s and Tian’s results. Only for $|S|=d+1$, we do not find the answer. We conjecture that any $l$ GBSs cannot be distinguished by one-way LOCC if $|S|=d+1$. If this conjecture is right, the problem about distinguishability of GBSs with one-way LOCC is completely solved in $d\otimes d$.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6974791">Cited in <strong>10</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A81P40" title="MSC2020">81P40</a> </td> <td class="space"> Quantum coherence, entanglement, quantum correlations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A81P50" title="MSC2020">81P50</a> </td> <td class="space"> Quantum state estimation, approximate cloning </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alocal+distinguishability">local distinguishability</a>; <a href="/?q=ut%3Amaximally+entangled+states">maximally entangled states</a>; <a href="/?q=ut%3Ageneralized+Bell+states">generalized Bell states</a>; <a href="/?q=ut%3Alocal+operations+and+classical+communication">local operations and classical communication</a></div> <div class="software"> <h3>Software:</h3><a href="/software/20493">QETLAB</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1402.81063" data-ciurl="/ci/06974791" data-biburl="/bibtex/06974791.bib" data-amsurl="/amsrefs/06974791.bib" data-xmlurl="/xml/06974791.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06974791.pdf" title="Zbl 1402.81063 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s11128-017-1797-2" aria-label="DOI for “Local distinguishability of generalized Bell states”" title="10.1007/s11128-017-1797-2">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bennett, CH; DiVincenzo, DP; Fuchs, CA; Mor, T; Rains, E; Shor, PW; Smolin, JA; Wootters, WK, Quantum nonlocality without entanglement, Phys. 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