Trace-2 excluded subsets of special linear groups over finite fields and mutually unbiased maximally entangled bases
Mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have a close relation with unitary 2-design and have attracted much attention in recent years. In the paper, we construct MUMEBs in C q ⊗ C q with q a power of an odd prime number. For this purpose, we introduce the notation o...
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| Veröffentlicht in: | Quantum information processing 2019-07, Vol.18 (7), p.1-13, Article 213 |
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| creator | Xu, Dengming |
| description | Mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have a close relation with unitary 2-design and have attracted much attention in recent years. In the paper, we construct MUMEBs in
C
q
⊗
C
q
with
q
a power of an odd prime number. For this purpose, we introduce the notation of trace-2 excluded subset of the special linear group
S
L
(
2
,
F
q
)
over the finite field
F
q
and establish a relation between a trace-2 excluded subset and a set of MUMEBs in
C
q
⊗
C
q
. Under this relation, we prove that
M
(
q
,
q
)
≥
q
2
-
1
2
by constructing trace-2 excluded subsets in
S
L
(
2
,
F
q
)
, which highly raises the lower bound of
M
(
q
,
q
) given in Liu et al. (Quantum Inf Process 16(6):159,
2017
) and Xu (Quantum Inf. Process 16(3):65,
2017
). |
| doi_str_mv | 10.1007/s11128-019-2330-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2227899209</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2227899209</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-354f516759b4ed8f8d7ff544a7ac3f2f556045233d80537a3c67ceb2c6bd81ba3</originalsourceid><addsrcrecordid>eNp1UEtLAzEQDqJgrf4AbwHP0Tw2ye5Rii8oeKnnkM2jbEl312Qj7b83dgVPnmaY7zEzHwC3BN8TjOVDIoTQGmHSIMoYRuIMLAiXDBHG6PmpxwhLzi_BVUo7jCkRtViAaRO1cYhCdzAhW2dhym1yU4KDh2l0ptMBhq53OsJtHPJYgC8Xoe_6bnKluGAT1L2F-zxlHcIR5r7tdCpOe33o9qeR6yfdb0OZtQVJ1-DC65DczW9dgo_np83qFa3fX95Wj2tkGBETYrzynAjJm7Zytva1ld7zqtJSG-ap51zgipd3bY05k5oZIY1rqRGtrUmr2RLczb5jHD6zS5PaDTn2ZaWilMq6aShuCovMLBOHlKLzaozl7nhUBKufcNUcrirhqp9wlSgaOmtS4fZbF_-c_xd9A-IMfgU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2227899209</pqid></control><display><type>article</type><title>Trace-2 excluded subsets of special linear groups over finite fields and mutually unbiased maximally entangled bases</title><source>SpringerLink Journals</source><creator>Xu, Dengming</creator><creatorcontrib>Xu, Dengming</creatorcontrib><description>Mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have a close relation with unitary 2-design and have attracted much attention in recent years. In the paper, we construct MUMEBs in
C
q
⊗
C
q
with
q
a power of an odd prime number. For this purpose, we introduce the notation of trace-2 excluded subset of the special linear group
S
L
(
2
,
F
q
)
over the finite field
F
q
and establish a relation between a trace-2 excluded subset and a set of MUMEBs in
C
q
⊗
C
q
. Under this relation, we prove that
M
(
q
,
q
)
≥
q
2
-
1
2
by constructing trace-2 excluded subsets in
S
L
(
2
,
F
q
)
, which highly raises the lower bound of
M
(
q
,
q
) given in Liu et al. (Quantum Inf Process 16(6):159,
2017
) and Xu (Quantum Inf. Process 16(3):65,
2017
).</description><identifier>ISSN: 1570-0755</identifier><identifier>EISSN: 1573-1332</identifier><identifier>DOI: 10.1007/s11128-019-2330-6</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Data Structures and Information Theory ; Fields (mathematics) ; Lower bounds ; Mathematical Physics ; Numbers ; Physics ; Physics and Astronomy ; Quantum Computing ; Quantum Information Technology ; Quantum Physics ; Spintronics</subject><ispartof>Quantum information processing, 2019-07, Vol.18 (7), p.1-13, Article 213</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-354f516759b4ed8f8d7ff544a7ac3f2f556045233d80537a3c67ceb2c6bd81ba3</citedby><cites>FETCH-LOGICAL-c316t-354f516759b4ed8f8d7ff544a7ac3f2f556045233d80537a3c67ceb2c6bd81ba3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11128-019-2330-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11128-019-2330-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Xu, Dengming</creatorcontrib><title>Trace-2 excluded subsets of special linear groups over finite fields and mutually unbiased maximally entangled bases</title><title>Quantum information processing</title><addtitle>Quantum Inf Process</addtitle><description>Mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have a close relation with unitary 2-design and have attracted much attention in recent years. In the paper, we construct MUMEBs in
C
q
⊗
C
q
with
q
a power of an odd prime number. For this purpose, we introduce the notation of trace-2 excluded subset of the special linear group
S
L
(
2
,
F
q
)
over the finite field
F
q
and establish a relation between a trace-2 excluded subset and a set of MUMEBs in
C
q
⊗
C
q
. Under this relation, we prove that
M
(
q
,
q
)
≥
q
2
-
1
2
by constructing trace-2 excluded subsets in
S
L
(
2
,
F
q
)
, which highly raises the lower bound of
M
(
q
,
q
) given in Liu et al. (Quantum Inf Process 16(6):159,
2017
) and Xu (Quantum Inf. Process 16(3):65,
2017
).</description><subject>Data Structures and Information Theory</subject><subject>Fields (mathematics)</subject><subject>Lower bounds</subject><subject>Mathematical Physics</subject><subject>Numbers</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Computing</subject><subject>Quantum Information Technology</subject><subject>Quantum Physics</subject><subject>Spintronics</subject><issn>1570-0755</issn><issn>1573-1332</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1UEtLAzEQDqJgrf4AbwHP0Tw2ye5Rii8oeKnnkM2jbEl312Qj7b83dgVPnmaY7zEzHwC3BN8TjOVDIoTQGmHSIMoYRuIMLAiXDBHG6PmpxwhLzi_BVUo7jCkRtViAaRO1cYhCdzAhW2dhym1yU4KDh2l0ptMBhq53OsJtHPJYgC8Xoe_6bnKluGAT1L2F-zxlHcIR5r7tdCpOe33o9qeR6yfdb0OZtQVJ1-DC65DczW9dgo_np83qFa3fX95Wj2tkGBETYrzynAjJm7Zytva1ld7zqtJSG-ap51zgipd3bY05k5oZIY1rqRGtrUmr2RLczb5jHD6zS5PaDTn2ZaWilMq6aShuCovMLBOHlKLzaozl7nhUBKufcNUcrirhqp9wlSgaOmtS4fZbF_-c_xd9A-IMfgU</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>Xu, Dengming</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190701</creationdate><title>Trace-2 excluded subsets of special linear groups over finite fields and mutually unbiased maximally entangled bases</title><author>Xu, Dengming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-354f516759b4ed8f8d7ff544a7ac3f2f556045233d80537a3c67ceb2c6bd81ba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Data Structures and Information Theory</topic><topic>Fields (mathematics)</topic><topic>Lower bounds</topic><topic>Mathematical Physics</topic><topic>Numbers</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Computing</topic><topic>Quantum Information Technology</topic><topic>Quantum Physics</topic><topic>Spintronics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xu, Dengming</creatorcontrib><collection>CrossRef</collection><jtitle>Quantum information processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xu, Dengming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Trace-2 excluded subsets of special linear groups over finite fields and mutually unbiased maximally entangled bases</atitle><jtitle>Quantum information processing</jtitle><stitle>Quantum Inf Process</stitle><date>2019-07-01</date><risdate>2019</risdate><volume>18</volume><issue>7</issue><spage>1</spage><epage>13</epage><pages>1-13</pages><artnum>213</artnum><issn>1570-0755</issn><eissn>1573-1332</eissn><abstract>Mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have a close relation with unitary 2-design and have attracted much attention in recent years. In the paper, we construct MUMEBs in
C
q
⊗
C
q
with
q
a power of an odd prime number. For this purpose, we introduce the notation of trace-2 excluded subset of the special linear group
S
L
(
2
,
F
q
)
over the finite field
F
q
and establish a relation between a trace-2 excluded subset and a set of MUMEBs in
C
q
⊗
C
q
. Under this relation, we prove that
M
(
q
,
q
)
≥
q
2
-
1
2
by constructing trace-2 excluded subsets in
S
L
(
2
,
F
q
)
, which highly raises the lower bound of
M
(
q
,
q
) given in Liu et al. (Quantum Inf Process 16(6):159,
2017
) and Xu (Quantum Inf. Process 16(3):65,
2017
).</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11128-019-2330-6</doi><tpages>13</tpages></addata></record> |
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| ispartof | Quantum information processing, 2019-07, Vol.18 (7), p.1-13, Article 213 |
| issn | 1570-0755 1573-1332 |
| language | eng |
| recordid | cdi_proquest_journals_2227899209 |
| source | SpringerLink Journals |
| subjects | Data Structures and Information Theory Fields (mathematics) Lower bounds Mathematical Physics Numbers Physics Physics and Astronomy Quantum Computing Quantum Information Technology Quantum Physics Spintronics |
| title | Trace-2 excluded subsets of special linear groups over finite fields and mutually unbiased maximally entangled bases |
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