Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices
We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system C d ⊗ C d ( d ≥ 3 ) with d a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct 2 ( d - 1 ) MUMEBs in C d ⊗ C d . It follows that M ( d , d ) ≥ 2 ( d - 1 ) , wh...
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| Veröffentlicht in: | Quantum information processing 2017-03, Vol.16 (3), p.1-11, Article 65 |
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| creator | xu, Dengming |
| description | We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system
C
d
⊗
C
d
(
d
≥
3
)
with
d
a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct
2
(
d
-
1
)
MUMEBs in
C
d
⊗
C
d
. It follows that
M
(
d
,
d
)
≥
2
(
d
-
1
)
, which is twice the number given in Liu et al. (
2016
), where
M
(
d
,
d
) denotes the maximal size of all sets of MUMEBs in
C
d
⊗
C
d
. In addition, let
q
be another power of a prime number, we construct MUMEBs in
C
d
⊗
C
q
d
from those in
C
d
⊗
C
d
by the use of the tensor product of unitary matrices. |
| doi_str_mv | 10.1007/s11128-017-1534-x |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1880759466</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1880759466</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-bd31577e04880ae11bd4e817c9988703dcdbbbadf90dfa0c55fc55c85f4969ca3</originalsourceid><addsrcrecordid>eNp1kMtOwzAQRS0EEqXwAewisTZ44jh2lqgCilSJDawtx3baVHkUP6T273EaFmxYWLbG956ZuQjdA3kEQviTB4BcYAIcA6MFPl6gBTBOMVCaX57fBBPO2DW68X5PSA6lKBfIrsbBBxd1aMchG5usjyGqrjtlcahb5a3JenVs-3PJDkEN2y7V6vTjs7BzY9zusoN1yaYmhJ8Ya2VUr9xkDa7V1t-iq0Z13t793kv09fryuVrjzcfb--p5gzWFMuDa0DQnt6QQgigLUJvCCuC6qoTghBpt6rpWpqmIaRTRjDXpaMGaoiorregSPczcgxu_o_VB7sfohtRSQkJyVhVlmVQwq7QbvXe2kQeXNnQnCUROaco5TZnSlFOa8pg8-ezxSTtsrftD_tf0A67wevs</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1880759466</pqid></control><display><type>article</type><title>Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices</title><source>SpringerLink Journals - AutoHoldings</source><creator>xu, Dengming</creator><creatorcontrib>xu, Dengming</creatorcontrib><description>We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system
C
d
⊗
C
d
(
d
≥
3
)
with
d
a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct
2
(
d
-
1
)
MUMEBs in
C
d
⊗
C
d
. It follows that
M
(
d
,
d
)
≥
2
(
d
-
1
)
, which is twice the number given in Liu et al. (
2016
), where
M
(
d
,
d
) denotes the maximal size of all sets of MUMEBs in
C
d
⊗
C
d
. In addition, let
q
be another power of a prime number, we construct MUMEBs in
C
d
⊗
C
q
d
from those in
C
d
⊗
C
d
by the use of the tensor product of unitary matrices.</description><identifier>ISSN: 1570-0755</identifier><identifier>EISSN: 1573-1332</identifier><identifier>DOI: 10.1007/s11128-017-1534-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Data Structures and Information Theory ; Mathematical Physics ; Permutations ; Physics ; Physics and Astronomy ; Prime numbers ; Quantum Computing ; Quantum Information Technology ; Quantum Physics ; Spintronics</subject><ispartof>Quantum information processing, 2017-03, Vol.16 (3), p.1-11, Article 65</ispartof><rights>Springer Science+Business Media New York 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-bd31577e04880ae11bd4e817c9988703dcdbbbadf90dfa0c55fc55c85f4969ca3</citedby><cites>FETCH-LOGICAL-c316t-bd31577e04880ae11bd4e817c9988703dcdbbbadf90dfa0c55fc55c85f4969ca3</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/s11128-017-1534-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11128-017-1534-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>xu, Dengming</creatorcontrib><title>Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices</title><title>Quantum information processing</title><addtitle>Quantum Inf Process</addtitle><description>We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system
C
d
⊗
C
d
(
d
≥
3
)
with
d
a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct
2
(
d
-
1
)
MUMEBs in
C
d
⊗
C
d
. It follows that
M
(
d
,
d
)
≥
2
(
d
-
1
)
, which is twice the number given in Liu et al. (
2016
), where
M
(
d
,
d
) denotes the maximal size of all sets of MUMEBs in
C
d
⊗
C
d
. In addition, let
q
be another power of a prime number, we construct MUMEBs in
C
d
⊗
C
q
d
from those in
C
d
⊗
C
d
by the use of the tensor product of unitary matrices.</description><subject>Data Structures and Information Theory</subject><subject>Mathematical Physics</subject><subject>Permutations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Prime numbers</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>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRS0EEqXwAewisTZ44jh2lqgCilSJDawtx3baVHkUP6T273EaFmxYWLbG956ZuQjdA3kEQviTB4BcYAIcA6MFPl6gBTBOMVCaX57fBBPO2DW68X5PSA6lKBfIrsbBBxd1aMchG5usjyGqrjtlcahb5a3JenVs-3PJDkEN2y7V6vTjs7BzY9zusoN1yaYmhJ8Ya2VUr9xkDa7V1t-iq0Z13t793kv09fryuVrjzcfb--p5gzWFMuDa0DQnt6QQgigLUJvCCuC6qoTghBpt6rpWpqmIaRTRjDXpaMGaoiorregSPczcgxu_o_VB7sfohtRSQkJyVhVlmVQwq7QbvXe2kQeXNnQnCUROaco5TZnSlFOa8pg8-ezxSTtsrftD_tf0A67wevs</recordid><startdate>20170301</startdate><enddate>20170301</enddate><creator>xu, Dengming</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170301</creationdate><title>Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices</title><author>xu, Dengming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-bd31577e04880ae11bd4e817c9988703dcdbbbadf90dfa0c55fc55c85f4969ca3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Data Structures and Information Theory</topic><topic>Mathematical Physics</topic><topic>Permutations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Prime numbers</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>Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices</atitle><jtitle>Quantum information processing</jtitle><stitle>Quantum Inf Process</stitle><date>2017-03-01</date><risdate>2017</risdate><volume>16</volume><issue>3</issue><spage>1</spage><epage>11</epage><pages>1-11</pages><artnum>65</artnum><issn>1570-0755</issn><eissn>1573-1332</eissn><abstract>We construct mutually unbiased maximally entangled bases (MUMEBs) in bipartite system
C
d
⊗
C
d
(
d
≥
3
)
with
d
a power of a prime number. Precisely, by means of permutation matrices and Hadamard matrices, we construct
2
(
d
-
1
)
MUMEBs in
C
d
⊗
C
d
. It follows that
M
(
d
,
d
)
≥
2
(
d
-
1
)
, which is twice the number given in Liu et al. (
2016
), where
M
(
d
,
d
) denotes the maximal size of all sets of MUMEBs in
C
d
⊗
C
d
. In addition, let
q
be another power of a prime number, we construct MUMEBs in
C
d
⊗
C
q
d
from those in
C
d
⊗
C
d
by the use of the tensor product of unitary matrices.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11128-017-1534-x</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Quantum information processing, 2017-03, Vol.16 (3), p.1-11, Article 65 |
| issn | 1570-0755 1573-1332 |
| language | eng |
| recordid | cdi_proquest_journals_1880759466 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Data Structures and Information Theory Mathematical Physics Permutations Physics Physics and Astronomy Prime numbers Quantum Computing Quantum Information Technology Quantum Physics Spintronics |
| title | Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices |
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