Maximally entangled mixed states for qubit-qutrit systems

We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2016-12
Main Authors: Paulo E M F Mendonca, Marchiolli, Marcelo A, Hedemann, Samuel R
Format: Article
Language:English
Subjects:
Density
Optimization
Purity
Quantum entanglement
Semidefinite programming
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Paulo E M F Mendonca
Marchiolli, Marcelo A
Hedemann, Samuel R
description We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank-deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically-motivated assumptions, we provide strong numerical evidence that three-fold degenerate X states of purity \(P\) reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.
doi_str_mv 10.48550/arxiv.1612.01214
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2074636579</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2074636579</sourcerecordid><originalsourceid>FETCH-LOGICAL-a529-88c45a332b9d9c7b1f3c7f63ffd4089eed7badadc43045935ea9ed3241acda683</originalsourceid><addsrcrecordid>eNotjclqwzAUAEWh0JDmA3oz9GxXek_rsYRukNBL7uHZkoqDl8aSi_P3DbSXmdsMYw-CV9IqxZ9oWtqfSmgBFRcg5A1bAaIorQS4Y5uUTpxz0AaUwhVze1ranrruUoQh0_DVBV_07XJlypRDKuI4Fee5bnN5nvPU5iJdUg59ume3kboUNv9es8Pry2H7Xu4-3z62z7uSFLjS2kYqQoTaedeYWkRsTNQYo5fcuhC8qcmTbyRyqRyqQC54BCmo8aQtrtnjX_Z7Gs9zSPl4GudpuB6PwI3UqJVx-AurK0mw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2074636579</pqid></control><display><type>article</type><title>Maximally entangled mixed states for qubit-qutrit systems</title><source>Publicly Available Content Database</source><creator>Paulo E M F Mendonca ; Marchiolli, Marcelo A ; Hedemann, Samuel R</creator><creatorcontrib>Paulo E M F Mendonca ; Marchiolli, Marcelo A ; Hedemann, Samuel R</creatorcontrib><description>We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank-deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically-motivated assumptions, we provide strong numerical evidence that three-fold degenerate X states of purity \(P\) reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1612.01214</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Density ; Optimization ; Purity ; Quantum entanglement ; Semidefinite programming</subject><ispartof>arXiv.org, 2016-12</ispartof><rights>2016. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2074636579?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>776,780,25731,27902,36989,44566</link.rule.ids></links><search><creatorcontrib>Paulo E M F Mendonca</creatorcontrib><creatorcontrib>Marchiolli, Marcelo A</creatorcontrib><creatorcontrib>Hedemann, Samuel R</creatorcontrib><title>Maximally entangled mixed states for qubit-qutrit systems</title><title>arXiv.org</title><description>We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank-deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically-motivated assumptions, we provide strong numerical evidence that three-fold degenerate X states of purity \(P\) reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.</description><subject>Density</subject><subject>Optimization</subject><subject>Purity</subject><subject>Quantum entanglement</subject><subject>Semidefinite programming</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNotjclqwzAUAEWh0JDmA3oz9GxXek_rsYRukNBL7uHZkoqDl8aSi_P3DbSXmdsMYw-CV9IqxZ9oWtqfSmgBFRcg5A1bAaIorQS4Y5uUTpxz0AaUwhVze1ranrruUoQh0_DVBV_07XJlypRDKuI4Fee5bnN5nvPU5iJdUg59ume3kboUNv9es8Pry2H7Xu4-3z62z7uSFLjS2kYqQoTaedeYWkRsTNQYo5fcuhC8qcmTbyRyqRyqQC54BCmo8aQtrtnjX_Z7Gs9zSPl4GudpuB6PwI3UqJVx-AurK0mw</recordid><startdate>20161205</startdate><enddate>20161205</enddate><creator>Paulo E M F Mendonca</creator><creator>Marchiolli, Marcelo A</creator><creator>Hedemann, Samuel R</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20161205</creationdate><title>Maximally entangled mixed states for qubit-qutrit systems</title><author>Paulo E M F Mendonca ; Marchiolli, Marcelo A ; Hedemann, Samuel R</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a529-88c45a332b9d9c7b1f3c7f63ffd4089eed7badadc43045935ea9ed3241acda683</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Density</topic><topic>Optimization</topic><topic>Purity</topic><topic>Quantum entanglement</topic><topic>Semidefinite programming</topic><toplevel>online_resources</toplevel><creatorcontrib>Paulo E M F Mendonca</creatorcontrib><creatorcontrib>Marchiolli, Marcelo A</creatorcontrib><creatorcontrib>Hedemann, Samuel R</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering collection</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Paulo E M F Mendonca</au><au>Marchiolli, Marcelo A</au><au>Hedemann, Samuel R</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Maximally entangled mixed states for qubit-qutrit systems</atitle><jtitle>arXiv.org</jtitle><date>2016-12-05</date><risdate>2016</risdate><eissn>2331-8422</eissn><abstract>We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank-deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically-motivated assumptions, we provide strong numerical evidence that three-fold degenerate X states of purity \(P\) reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1612.01214</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2016-12
issn 2331-8422
language eng
recordid cdi_proquest_journals_2074636579
source Publicly Available Content Database
subjects Density
Optimization
Purity
Quantum entanglement
Semidefinite programming
title Maximally entangled mixed states for qubit-qutrit systems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T15%3A24%3A53IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Maximally%20entangled%20mixed%20states%20for%20qubit-qutrit%20systems&rft.jtitle=arXiv.org&rft.au=Paulo%20E%20M%20F%20Mendonca&rft.date=2016-12-05&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1612.01214&rft_dat=%3Cproquest%3E2074636579%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a529-88c45a332b9d9c7b1f3c7f63ffd4089eed7badadc43045935ea9ed3241acda683%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2074636579&rft_id=info:pmid/&rfr_iscdi=true