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Entanglement witness criteria of strong-k-separability for multipartite quantum states
Let H 1 , H 2 , … , H n be separable complex Hilbert spaces with dim H i ≥ 2 and n ≥ 2 . Assume that ρ is a state in H = H 1 ⊗ H 2 ⊗ ⋯ ⊗ H n . ρ is called strong- k -separable ( 2 ≤ k ≤ n ) if ρ is separable for any k -partite division of H . In this paper, an entanglement witnesses criterion of str...
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| Published in: | Quantum information processing 2018-07, Vol.17 (7), p.1-8, Article 181 |
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| container_title | Quantum information processing |
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| creator | Yan, Siqing Hou, Jinchuan |
| description | Let
H
1
,
H
2
,
…
,
H
n
be separable complex Hilbert spaces with
dim
H
i
≥
2
and
n
≥
2
. Assume that
ρ
is a state in
H
=
H
1
⊗
H
2
⊗
⋯
⊗
H
n
.
ρ
is called strong-
k
-separable
(
2
≤
k
≤
n
)
if
ρ
is separable for any
k
-partite division of
H
. In this paper, an entanglement witnesses criterion of strong-
k
-separability is obtained, which says that
ρ
is not strong-
k
-separable if and only if there exist a
k
-division space
H
m
1
⊗
⋯
⊗
H
m
k
of
H
, a finite-rank linear elementary operator positive on product states
Λ
:
B
(
H
m
2
⊗
⋯
⊗
H
m
k
)
→
B
(
H
m
1
)
and a state
ρ
0
∈
S
(
H
m
1
⊗
H
m
1
)
, such that
Tr
(
W
ρ
)
<
0
, where
W
=
(
Id
⊗
Λ
†
)
ρ
0
is an entanglement witness. In addition, several different methods of constructing entanglement witnesses for multipartite states are also given. |
| doi_str_mv | 10.1007/s11128-018-1952-4 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2053433079</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2053433079</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-4e3e5cec07b9109e7fa7a738766026d7d82ba59610286b1c29cb591feb26440d3</originalsourceid><addsrcrecordid>eNp1kEFLwzAUx4MoOKcfwFvBc_S9pEnao4zphIEX9RrSLh2dbbolKbJvb2YFT57e4_H7_x_8CLlFuEcA9RAQkRUUsKBYCkbzMzJDoThFztn5zw4UlBCX5CqEHQBDWcgZ-Vi6aNy2s711Mftqo7MhZLVvo_WtyYYmC9EPbks_abB7403Vdm08Zs3gs37sYptuMcHZYTQujn3CTbThmlw0pgv25nfOyfvT8m2xouvX55fF45rWHGWkueVW1LYGVZUIpVWNUUbxQkkJTG7UpmCVEaVEYIWssGZlXYkSG1sxmeew4XNyN_Xu_XAYbYh6N4zepZeageA556DKROFE1X4IwdtG733bG3_UCPqkT0_6dNKnT_p0njJsyoTEuq31f83_h74BUI5zgg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2053433079</pqid></control><display><type>article</type><title>Entanglement witness criteria of strong-k-separability for multipartite quantum states</title><source>Springer Nature</source><creator>Yan, Siqing ; Hou, Jinchuan</creator><creatorcontrib>Yan, Siqing ; Hou, Jinchuan</creatorcontrib><description>Let
H
1
,
H
2
,
…
,
H
n
be separable complex Hilbert spaces with
dim
H
i
≥
2
and
n
≥
2
. Assume that
ρ
is a state in
H
=
H
1
⊗
H
2
⊗
⋯
⊗
H
n
.
ρ
is called strong-
k
-separable
(
2
≤
k
≤
n
)
if
ρ
is separable for any
k
-partite division of
H
. In this paper, an entanglement witnesses criterion of strong-
k
-separability is obtained, which says that
ρ
is not strong-
k
-separable if and only if there exist a
k
-division space
H
m
1
⊗
⋯
⊗
H
m
k
of
H
, a finite-rank linear elementary operator positive on product states
Λ
:
B
(
H
m
2
⊗
⋯
⊗
H
m
k
)
→
B
(
H
m
1
)
and a state
ρ
0
∈
S
(
H
m
1
⊗
H
m
1
)
, such that
Tr
(
W
ρ
)
<
0
, where
W
=
(
Id
⊗
Λ
†
)
ρ
0
is an entanglement witness. In addition, several different methods of constructing entanglement witnesses for multipartite states are also given.</description><identifier>ISSN: 1570-0755</identifier><identifier>EISSN: 1573-1332</identifier><identifier>DOI: 10.1007/s11128-018-1952-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Data Structures and Information Theory ; Hilbert space ; Mathematical Physics ; Physics ; Physics and Astronomy ; Quantum Computing ; Quantum entanglement ; Quantum Information Technology ; Quantum Physics ; Quantum theory ; Spintronics</subject><ispartof>Quantum information processing, 2018-07, Vol.17 (7), p.1-8, Article 181</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-4e3e5cec07b9109e7fa7a738766026d7d82ba59610286b1c29cb591feb26440d3</citedby><cites>FETCH-LOGICAL-c316t-4e3e5cec07b9109e7fa7a738766026d7d82ba59610286b1c29cb591feb26440d3</cites><orcidid>0000-0003-1741-0711</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Yan, Siqing</creatorcontrib><creatorcontrib>Hou, Jinchuan</creatorcontrib><title>Entanglement witness criteria of strong-k-separability for multipartite quantum states</title><title>Quantum information processing</title><addtitle>Quantum Inf Process</addtitle><description>Let
H
1
,
H
2
,
…
,
H
n
be separable complex Hilbert spaces with
dim
H
i
≥
2
and
n
≥
2
. Assume that
ρ
is a state in
H
=
H
1
⊗
H
2
⊗
⋯
⊗
H
n
.
ρ
is called strong-
k
-separable
(
2
≤
k
≤
n
)
if
ρ
is separable for any
k
-partite division of
H
. In this paper, an entanglement witnesses criterion of strong-
k
-separability is obtained, which says that
ρ
is not strong-
k
-separable if and only if there exist a
k
-division space
H
m
1
⊗
⋯
⊗
H
m
k
of
H
, a finite-rank linear elementary operator positive on product states
Λ
:
B
(
H
m
2
⊗
⋯
⊗
H
m
k
)
→
B
(
H
m
1
)
and a state
ρ
0
∈
S
(
H
m
1
⊗
H
m
1
)
, such that
Tr
(
W
ρ
)
<
0
, where
W
=
(
Id
⊗
Λ
†
)
ρ
0
is an entanglement witness. In addition, several different methods of constructing entanglement witnesses for multipartite states are also given.</description><subject>Data Structures and Information Theory</subject><subject>Hilbert space</subject><subject>Mathematical Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Computing</subject><subject>Quantum entanglement</subject><subject>Quantum Information Technology</subject><subject>Quantum Physics</subject><subject>Quantum theory</subject><subject>Spintronics</subject><issn>1570-0755</issn><issn>1573-1332</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLwzAUx4MoOKcfwFvBc_S9pEnao4zphIEX9RrSLh2dbbolKbJvb2YFT57e4_H7_x_8CLlFuEcA9RAQkRUUsKBYCkbzMzJDoThFztn5zw4UlBCX5CqEHQBDWcgZ-Vi6aNy2s711Mftqo7MhZLVvo_WtyYYmC9EPbks_abB7403Vdm08Zs3gs37sYptuMcHZYTQujn3CTbThmlw0pgv25nfOyfvT8m2xouvX55fF45rWHGWkueVW1LYGVZUIpVWNUUbxQkkJTG7UpmCVEaVEYIWssGZlXYkSG1sxmeew4XNyN_Xu_XAYbYh6N4zepZeageA556DKROFE1X4IwdtG733bG3_UCPqkT0_6dNKnT_p0njJsyoTEuq31f83_h74BUI5zgg</recordid><startdate>20180701</startdate><enddate>20180701</enddate><creator>Yan, Siqing</creator><creator>Hou, Jinchuan</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1741-0711</orcidid></search><sort><creationdate>20180701</creationdate><title>Entanglement witness criteria of strong-k-separability for multipartite quantum states</title><author>Yan, Siqing ; Hou, Jinchuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-4e3e5cec07b9109e7fa7a738766026d7d82ba59610286b1c29cb591feb26440d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Data Structures and Information Theory</topic><topic>Hilbert space</topic><topic>Mathematical Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Computing</topic><topic>Quantum entanglement</topic><topic>Quantum Information Technology</topic><topic>Quantum Physics</topic><topic>Quantum theory</topic><topic>Spintronics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yan, Siqing</creatorcontrib><creatorcontrib>Hou, Jinchuan</creatorcontrib><collection>CrossRef</collection><jtitle>Quantum information processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yan, Siqing</au><au>Hou, Jinchuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Entanglement witness criteria of strong-k-separability for multipartite quantum states</atitle><jtitle>Quantum information processing</jtitle><stitle>Quantum Inf Process</stitle><date>2018-07-01</date><risdate>2018</risdate><volume>17</volume><issue>7</issue><spage>1</spage><epage>8</epage><pages>1-8</pages><artnum>181</artnum><issn>1570-0755</issn><eissn>1573-1332</eissn><abstract>Let
H
1
,
H
2
,
…
,
H
n
be separable complex Hilbert spaces with
dim
H
i
≥
2
and
n
≥
2
. Assume that
ρ
is a state in
H
=
H
1
⊗
H
2
⊗
⋯
⊗
H
n
.
ρ
is called strong-
k
-separable
(
2
≤
k
≤
n
)
if
ρ
is separable for any
k
-partite division of
H
. In this paper, an entanglement witnesses criterion of strong-
k
-separability is obtained, which says that
ρ
is not strong-
k
-separable if and only if there exist a
k
-division space
H
m
1
⊗
⋯
⊗
H
m
k
of
H
, a finite-rank linear elementary operator positive on product states
Λ
:
B
(
H
m
2
⊗
⋯
⊗
H
m
k
)
→
B
(
H
m
1
)
and a state
ρ
0
∈
S
(
H
m
1
⊗
H
m
1
)
, such that
Tr
(
W
ρ
)
<
0
, where
W
=
(
Id
⊗
Λ
†
)
ρ
0
is an entanglement witness. In addition, several different methods of constructing entanglement witnesses for multipartite states are also given.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11128-018-1952-4</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0003-1741-0711</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1570-0755 |
| ispartof | Quantum information processing, 2018-07, Vol.17 (7), p.1-8, Article 181 |
| issn | 1570-0755 1573-1332 |
| language | eng |
| recordid | cdi_proquest_journals_2053433079 |
| source | Springer Nature |
| subjects | Data Structures and Information Theory Hilbert space Mathematical Physics Physics Physics and Astronomy Quantum Computing Quantum entanglement Quantum Information Technology Quantum Physics Quantum theory Spintronics |
| title | Entanglement witness criteria of strong-k-separability for multipartite quantum states |
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