Polarization-transverse-spatial logical qubit entanglement purification using linear optics

We propose two types of logical qubit entanglement purification protocols (LEPPs) to reduce the effect of noises inside and outside the logical qubit subspace using linear optics, where logical qubit is encoded by single-photon polarization-transverse-spatial Bell state. For the noise outside of the...

Full description

Saved in:
Bibliographic Details
Published inOptics and laser technology Vol. 185; p. 112566
Main Authors Guo, Peng-Liang, Gao, Cheng-Yan, Ren, Bao-Cang
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2025
Subjects
Online AccessGet full text

Cover

Loading…
Abstract We propose two types of logical qubit entanglement purification protocols (LEPPs) to reduce the effect of noises inside and outside the logical qubit subspace using linear optics, where logical qubit is encoded by single-photon polarization-transverse-spatial Bell state. For the noise outside of the logical qubit subspace, deterministic LEPP is presented to determine and correct the error-entangled state using error correction of the single-photon Bell state, resulting in the logical entangled state with unity fidelity. For the noise inside of the logical qubit subspace, probabilistic LEPP is presented to progressively increase the fidelity of the noisy logical entangled state using the parity and diagonal-basis measurements for the logical qubit. These two types of LEPPs have experimental feasibility with current technology, and the quantum operations of logical qubits in these protocols have fantastic applications in some other logical-encoding quantum information protocols.
AbstractList We propose two types of logical qubit entanglement purification protocols (LEPPs) to reduce the effect of noises inside and outside the logical qubit subspace using linear optics, where logical qubit is encoded by single-photon polarization-transverse-spatial Bell state. For the noise outside of the logical qubit subspace, deterministic LEPP is presented to determine and correct the error-entangled state using error correction of the single-photon Bell state, resulting in the logical entangled state with unity fidelity. For the noise inside of the logical qubit subspace, probabilistic LEPP is presented to progressively increase the fidelity of the noisy logical entangled state using the parity and diagonal-basis measurements for the logical qubit. These two types of LEPPs have experimental feasibility with current technology, and the quantum operations of logical qubits in these protocols have fantastic applications in some other logical-encoding quantum information protocols.
ArticleNumber 112566
Author Guo, Peng-Liang
Ren, Bao-Cang
Gao, Cheng-Yan
Author_xml – sequence: 1
  givenname: Peng-Liang
  surname: Guo
  fullname: Guo, Peng-Liang
  email: guopengliang@tynu.edu.cn
  organization: Department of Physics, Taiyuan Normal University, Jinzhong, 030619, Shanxi, China
– sequence: 2
  givenname: Cheng-Yan
  surname: Gao
  fullname: Gao, Cheng-Yan
  organization: Department of Physics, Taiyuan Normal University, Jinzhong, 030619, Shanxi, China
– sequence: 3
  givenname: Bao-Cang
  orcidid: 0000-0002-7679-3612
  surname: Ren
  fullname: Ren, Bao-Cang
  email: renbaocang@cnu.edu.cn
  organization: Department of Physics, Capital Normal University, Beijing, 100048, China
BookMark eNqFkM1OwzAQhH0oEm3hGcgLJHjtJCXHquJPqgQHOHGw1s6mcpXawXYrwdOTKogrp1ntaEajb8Fmzjti7AZ4ARzq233hh9RjTGQKwUVVAIiqrmdszrnkuWwacckWMe4552VdyTn7ePU9BvuNyXqXp4AunihEyuMwvrDPer-zZtTPo7YpI5fQ7Xo6jEc2HIPtRvMczY7Rul3WW0cYsnGFNfGKXXTYR7r-1SV7f7h_2zzl25fH5816mxtoIOUCKy2pFNDJGrq7shaN0ICAXNOq5SvQnYSyFNKAadoKS9K6QyOQBJclSLlkq6nXBB9joE4NwR4wfCng6sxF7dUfF3XmoiYuY3I9JWmcd7IUVDSWnKHWBjJJtd7-2_ED-nt3SQ
Cites_doi 10.1007/s11128-022-03646-y
10.1038/35074041
10.1103/PhysRevLett.77.2818
10.1103/PhysRevLett.126.010503
10.1103/PhysRevLett.67.661
10.1103/PhysRevLett.127.040502
10.1103/PhysRevLett.76.722
10.1038/ncomms1951
10.1038/nature01623
10.1103/PhysRevLett.70.1895
10.1002/andp.202200505
10.1103/PhysRevA.81.032307
10.1103/PhysRevA.82.044304
10.1038/nature05146
10.1103/PhysRevA.109.042423
10.1364/JOSAB.397973
10.1364/OE.394617
10.1103/PhysRevLett.118.220501
10.1103/PhysRevA.80.042308
10.1103/PhysRevA.66.014301
10.1103/PhysRevA.65.032302
10.1038/nphoton.2012.243
10.1103/RevModPhys.92.025002
10.1007/s11433-023-2245-9
10.1016/j.aop.2017.07.012
10.1364/OE.23.009284
10.1126/science.aan0070
10.1103/PhysRevA.97.022321
10.1007/s11128-023-03852-2
10.1103/PhysRevLett.106.110402
10.1103/PhysRevLett.89.257901
10.1002/que2.13
10.1016/j.scib.2021.12.018
10.1103/PhysRevLett.69.2881
10.1038/s41566-017-0010-6
10.1364/OE.374292
10.1103/PhysRevLett.114.113603
10.1103/PhysRevLett.110.260503
10.1088/0034-4885/70/8/R03
10.1103/PhysRevLett.112.250501
10.1103/PhysRevA.104.012419
10.1007/s43673-021-00017-0
10.1007/s11128-023-04097-9
10.1103/PhysRevA.86.023815
10.1103/PhysRevA.77.032345
10.1103/PhysRevA.65.022304
10.22331/q-2019-02-18-123
10.1103/PhysRevA.63.042307
10.1364/OE.25.002969
10.1038/srep28813
10.1103/PhysRevA.105.062418
10.1103/PhysRevLett.68.557
10.1103/PhysRevA.98.042309
10.1103/PhysRevA.68.012323
10.1088/1612-202X/ad1aaa
10.1103/PhysRevA.72.032313
10.1103/PhysRevLett.98.100501
10.1038/nphoton.2010.35
10.1007/s11128-024-04505-8
10.1103/PhysRevA.54.3824
10.1007/s11433-023-2258-x
10.1103/RevModPhys.74.145
10.1007/s11128-024-04271-7
10.1016/j.physleta.2011.09.056
10.1007/s11433-022-2065-x
10.1007/s11433-021-1863-9
10.1038/37539
10.1103/PhysRevA.90.052309
10.1364/OPTICA.4.001006
10.1103/PhysRevA.71.062325
10.1103/PhysRevA.68.042317
10.1016/j.scib.2021.11.002
10.1103/PhysRevLett.127.040506
10.1364/OE.383499
ContentType Journal Article
Copyright 2025 Elsevier Ltd
Copyright_xml – notice: 2025 Elsevier Ltd
DBID AAYXX
CITATION
DOI 10.1016/j.optlastec.2025.112566
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Physics
ExternalDocumentID 10_1016_j_optlastec_2025_112566
S0030399225001549
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
123
1B1
1RT
1~.
1~5
29N
4.4
457
4G.
53G
5VS
7-5
71M
8P~
9JN
AABXZ
AACTN
AAEDT
AAEDW
AAEPC
AAIKC
AAIKJ
AAKOC
AALRI
AAMNW
AAOAW
AAQFI
AAQXK
AAXKI
AAXUO
ABDPE
ABJNI
ABMAC
ABNEU
ABWVN
ABXDB
ABXRA
ACBEA
ACDAQ
ACFVG
ACGFO
ACGFS
ACIWK
ACNNM
ACRLP
ACRPL
ADBBV
ADEZE
ADMUD
ADNMO
ADTZH
AEBSH
AECPX
AEIPS
AEKER
AENEX
AEZYN
AFFNX
AFJKZ
AFRZQ
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AIEXJ
AIKHN
AITUG
AIVDX
AKRWK
ALMA_UNASSIGNED_HOLDINGS
AMRAJ
ANKPU
ASPBG
AVWKF
AXJTR
AZFZN
BBWZM
BJAXD
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EJD
EO8
EO9
EP2
EP3
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HMV
HVGLF
HZ~
IHE
J1W
JJJVA
KOM
LY7
M38
M41
MAGPM
MO0
N9A
NDZJH
O-L
O9-
OAUVE
OGIMB
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SET
SEW
SPC
SPCBC
SPD
SPG
SSM
SSQ
SST
SSZ
T5K
TN5
UHS
WH7
WUQ
ZMT
~G-
AATTM
AAYWO
AAYXX
ACVFH
ADCNI
AEUPX
AFPUW
AFXIZ
AGCQF
AGQPQ
AGRNS
AIGII
AIIUN
AKBMS
AKYEP
APXCP
BNPGV
CITATION
SSH
ID FETCH-LOGICAL-c191t-2a5b3e421f361f846292b1a1a0be7d071bf314423c1c9d5a4ebbfac2ae2034133
IEDL.DBID .~1
ISSN 0030-3992
IngestDate Tue Jul 01 05:26:04 EDT 2025
Sat Mar 15 15:40:40 EDT 2025
IsPeerReviewed true
IsScholarly true
Keywords Entanglement purification
Error correction
Logical qubit
Linear optics
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c191t-2a5b3e421f361f846292b1a1a0be7d071bf314423c1c9d5a4ebbfac2ae2034133
ORCID 0000-0002-7679-3612
ParticipantIDs crossref_primary_10_1016_j_optlastec_2025_112566
elsevier_sciencedirect_doi_10_1016_j_optlastec_2025_112566
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate July 2025
2025-07-00
PublicationDateYYYYMMDD 2025-07-01
PublicationDate_xml – month: 07
  year: 2025
  text: July 2025
PublicationDecade 2020
PublicationTitle Optics and laser technology
PublicationYear 2025
Publisher Elsevier Ltd
Publisher_xml – name: Elsevier Ltd
References Sasada, Okamoto (b76) 2003; 68
Bombin, Martin-Delgado (b31) 2005; 72
Zhou, Sheng (b67) 2017; 385
Bouwmeester, Pan, Mattle, Eibl, Weinfurter, Zeilinger (b9) 1997; 390
Grudka, Wójcik (b13) 2002; 66
Gu, Feng, Du, Zhong, Sheng, Zhou (b23) 2024; 21
Sheng, Long, Deng (b46) 2012; 376
Li, Xie, Li, Liang, Li, Li (b62) 2024; 67
Bennett, Brassard, Mermin (b2) 1992; 68
Wang, Mi, Wang (b36) 2017; 25
Kempe, Bacon, Lidar, Whaley (b64) 2001; 63
Li (b45) 2010; 82
Ekert (b1) 1991; 67
Deng, Long, Liu (b15) 2003; 68
Chen, Yong, Xu, Yao, Xiang, Li, Liu, Lu, Liu, Li, Yang, Peng, Zhao, Chen, Pan (b53) 2017; 11
Souza, Borges, Khoury, Huguenin, Aolita, Walborn (b71) 2008; 77
Gao, Ma, Liu, Long, Li, Li (b75) 2020; 37
Fujii, Yamamoto (b33) 2009; 80
Sheng, Deng, Zhou (b32) 2008; 77
Wang, Liu, Zhang, Cao, Wang (b35) 2015; 23
Gisin, Ribordy, Tittel, Zbinden (b3) 2002; 74
Zhou, Zhong, Sheng (b41) 2020; 28
Passos, Balthazar, Khoury, Hor-Meyll, Davidovich, Huguenin (b77) 2018; 97
Riera-Sàbat, Sekatski, Pirker, Dür (b47) 2021; 127
Aolita, Walborn (b70) 2007; 98
Bennett, Brassard, Crépeau, Jozsa, Peres, Wootters (b8) 1993; 70
Krastanov, Albert, Jiang (b40) 2019; 3
Zhang, Ding, Sheng, Zhou, Shi, Guo (b16) 2017; 118
Xu, Ma, Zhang, Lo, Pan (b4) 2020; 92
Miguel-Ramiro, Dür (b39) 2018; 98
Osorio, Bruno, Sangouard, Zbinden, Gisin, Thew (b22) 2012; 86
Liu, Long, Tong, Li (b12) 2002; 65
Xiang, Ralph, Lund, Walk, Pryde (b21) 2010; 4
Riera-Sàbat, Sekatski, Pirker, Dür (b48) 2021; 104
Guo, Zhou, Zhang (b20) 2024; 23
Zhou, Sheng (b66) 2016; 6
Sit, Bouchard, Fickler, Gagnon-Bischoff, Larocque, Heshami, Elser, Peuntinger, Günthner, Heim, Marquardt, Leuchs, Boyd, Karimi (b73) 2017; 4
Bennett, Wiesner (b11) 1992; 69
Dür, Briegel (b27) 2007; 70
Zwerger, Briegel, Dür (b42) 2013; 110
Lidar, Birgitta Whaley (b65) 2003
Wang, Zhang, Yu, Yuan, Du, Ren (b43) 2023; 535
D’ambrosio, Nagali, Walborn, Aolita, Slussarenko, Marrucci, Sciarrino (b72) 2012; 3
Deutsch, Ekert, Jozsa, Macchiavello, Popescu, Sanpera (b28) 1996; 77
Sheng, Deng (b44) 2010; 81
Sheng, Zhou (b63) 2024; 67
Pan, Simon, Brukner, Zeilinger (b29) 2001; 410
Wang, Ai, Deng, Ren (b37) 2020; 28
Kwek, Cao, Luo, Wang, Sun, Wang, Liu (b5) 2021; 31
Vollbrecht, Verstraete (b30) 2005; 71
Simon, Pan (b38) 2002; 89
Ecker, Sohr, Bulla, Huber, Bohmann, Ursin (b55) 2021; 127
Xiao, Zhou, Zhong, Du, Sheng (b19) 2023; 22
Wang, Zhu (b7) 2024; 23
Bera, Gupta, Majumdar (b6) 2023; 22
Bennett, DiVincenzo, Smolin, Wootters (b26) 1996; 54
Long, Liu (b14) 2002; 65
Yan, Zhou, Zhong, Sheng (b68) 2022; 105
Huang, Hu, Liu, Zhou, Sheng, Li, Guo (b56) 2022; 67
Kalb, Reiserer, Humphreys, Bakermans, Kamerling, Nickerson, Benjamin, Twitchen, Markham, Hanson (b52) 2017; 356
Muralidharan, Kim, Lütkenhaus, Lukin, Jiang (b60) 2014; 112
Ren, Du, Deng (b34) 2014; 90
Bennett, Brassard, Popescu, Schumacher, Smolin, Wootters (b25) 1996; 76
Pan, Gasparoni, Ursin, Weihs, Zeilinger (b50) 2003; 423
Yan, Zhou, Zhong, Sheng (b24) 2023; 66
Hu, Zhang, Zhang, Liu, Huang, Han, Li, Guo (b10) 2019; 1
Munro, Stephens, Devitt, Harrison, Nemoto (b59) 2012; 6
Zhou, Sheng (b17) 2022; 65
Hu, Huang, Sheng, Zhou, Liu, Guo, Zhang, Xing, Huang, Li, Guo (b54) 2021; 126
Luo, Zhou, Zhong, Sheng (b69) 2022; 21
Wang, Ren, Byrd, Wu (b61) 2023; 108
Sheng, Zhou, Long (b18) 2022; 67
Lee, Park, Ralph, Jeong (b57) 2015; 114
Reichle, Leibfried, Knill, Britton, Blakestad, Jost, Langer, Ozeri, Seidelin, Wineland (b51) 2006; 443
Qi, Li, Yang, Yuan, Ren (b49) 2024; 109
Guo, Dong, He, Jing, He, Ren, Li, Deng (b74) 2020; 28
Fröwis, Dür (b58) 2011; 106
Dür (10.1016/j.optlastec.2025.112566_b27) 2007; 70
Pan (10.1016/j.optlastec.2025.112566_b50) 2003; 423
Xu (10.1016/j.optlastec.2025.112566_b4) 2020; 92
Guo (10.1016/j.optlastec.2025.112566_b20) 2024; 23
Lidar (10.1016/j.optlastec.2025.112566_b65) 2003
Liu (10.1016/j.optlastec.2025.112566_b12) 2002; 65
Long (10.1016/j.optlastec.2025.112566_b14) 2002; 65
Deng (10.1016/j.optlastec.2025.112566_b15) 2003; 68
Ren (10.1016/j.optlastec.2025.112566_b34) 2014; 90
Xiao (10.1016/j.optlastec.2025.112566_b19) 2023; 22
Li (10.1016/j.optlastec.2025.112566_b45) 2010; 82
Wang (10.1016/j.optlastec.2025.112566_b7) 2024; 23
Bennett (10.1016/j.optlastec.2025.112566_b8) 1993; 70
Guo (10.1016/j.optlastec.2025.112566_b74) 2020; 28
Wang (10.1016/j.optlastec.2025.112566_b43) 2023; 535
Passos (10.1016/j.optlastec.2025.112566_b77) 2018; 97
Bouwmeester (10.1016/j.optlastec.2025.112566_b9) 1997; 390
Wang (10.1016/j.optlastec.2025.112566_b35) 2015; 23
Yan (10.1016/j.optlastec.2025.112566_b68) 2022; 105
Bera (10.1016/j.optlastec.2025.112566_b6) 2023; 22
Souza (10.1016/j.optlastec.2025.112566_b71) 2008; 77
Kalb (10.1016/j.optlastec.2025.112566_b52) 2017; 356
Chen (10.1016/j.optlastec.2025.112566_b53) 2017; 11
Luo (10.1016/j.optlastec.2025.112566_b69) 2022; 21
Sheng (10.1016/j.optlastec.2025.112566_b44) 2010; 81
Sheng (10.1016/j.optlastec.2025.112566_b18) 2022; 67
Gu (10.1016/j.optlastec.2025.112566_b23) 2024; 21
Simon (10.1016/j.optlastec.2025.112566_b38) 2002; 89
Sheng (10.1016/j.optlastec.2025.112566_b46) 2012; 376
Ecker (10.1016/j.optlastec.2025.112566_b55) 2021; 127
Li (10.1016/j.optlastec.2025.112566_b62) 2024; 67
Grudka (10.1016/j.optlastec.2025.112566_b13) 2002; 66
Reichle (10.1016/j.optlastec.2025.112566_b51) 2006; 443
Hu (10.1016/j.optlastec.2025.112566_b54) 2021; 126
Riera-Sàbat (10.1016/j.optlastec.2025.112566_b47) 2021; 127
Fröwis (10.1016/j.optlastec.2025.112566_b58) 2011; 106
Kempe (10.1016/j.optlastec.2025.112566_b64) 2001; 63
Bennett (10.1016/j.optlastec.2025.112566_b26) 1996; 54
Krastanov (10.1016/j.optlastec.2025.112566_b40) 2019; 3
Hu (10.1016/j.optlastec.2025.112566_b10) 2019; 1
D’ambrosio (10.1016/j.optlastec.2025.112566_b72) 2012; 3
Bennett (10.1016/j.optlastec.2025.112566_b2) 1992; 68
Riera-Sàbat (10.1016/j.optlastec.2025.112566_b48) 2021; 104
Qi (10.1016/j.optlastec.2025.112566_b49) 2024; 109
Kwek (10.1016/j.optlastec.2025.112566_b5) 2021; 31
Deutsch (10.1016/j.optlastec.2025.112566_b28) 1996; 77
Fujii (10.1016/j.optlastec.2025.112566_b33) 2009; 80
Osorio (10.1016/j.optlastec.2025.112566_b22) 2012; 86
Gao (10.1016/j.optlastec.2025.112566_b75) 2020; 37
Sit (10.1016/j.optlastec.2025.112566_b73) 2017; 4
Zwerger (10.1016/j.optlastec.2025.112566_b42) 2013; 110
Miguel-Ramiro (10.1016/j.optlastec.2025.112566_b39) 2018; 98
Bombin (10.1016/j.optlastec.2025.112566_b31) 2005; 72
Sheng (10.1016/j.optlastec.2025.112566_b32) 2008; 77
Pan (10.1016/j.optlastec.2025.112566_b29) 2001; 410
Muralidharan (10.1016/j.optlastec.2025.112566_b60) 2014; 112
Zhou (10.1016/j.optlastec.2025.112566_b17) 2022; 65
Zhou (10.1016/j.optlastec.2025.112566_b41) 2020; 28
Bennett (10.1016/j.optlastec.2025.112566_b11) 1992; 69
Zhang (10.1016/j.optlastec.2025.112566_b16) 2017; 118
Aolita (10.1016/j.optlastec.2025.112566_b70) 2007; 98
Bennett (10.1016/j.optlastec.2025.112566_b25) 1996; 76
Huang (10.1016/j.optlastec.2025.112566_b56) 2022; 67
Xiang (10.1016/j.optlastec.2025.112566_b21) 2010; 4
Vollbrecht (10.1016/j.optlastec.2025.112566_b30) 2005; 71
Lee (10.1016/j.optlastec.2025.112566_b57) 2015; 114
Gisin (10.1016/j.optlastec.2025.112566_b3) 2002; 74
Wang (10.1016/j.optlastec.2025.112566_b36) 2017; 25
Yan (10.1016/j.optlastec.2025.112566_b24) 2023; 66
Sheng (10.1016/j.optlastec.2025.112566_b63) 2024; 67
Sasada (10.1016/j.optlastec.2025.112566_b76) 2003; 68
Ekert (10.1016/j.optlastec.2025.112566_b1) 1991; 67
Wang (10.1016/j.optlastec.2025.112566_b61) 2023; 108
Wang (10.1016/j.optlastec.2025.112566_b37) 2020; 28
Zhou (10.1016/j.optlastec.2025.112566_b67) 2017; 385
Munro (10.1016/j.optlastec.2025.112566_b59) 2012; 6
Zhou (10.1016/j.optlastec.2025.112566_b66) 2016; 6
References_xml – volume: 23
  start-page: 64
  year: 2024
  ident: b7
  article-title: A hybrid dynamic n-party quantum key exchange protocol based on three-particle GHZ states
  publication-title: Quantum Inf. Process.
– volume: 72
  year: 2005
  ident: b31
  article-title: Entanglement distillation protocols and number theory
  publication-title: Phys. Rev. A
– volume: 68
  year: 2003
  ident: b15
  article-title: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block
  publication-title: Phys. Rev. A
– volume: 22
  start-page: 109
  year: 2023
  ident: b6
  article-title: Device-independent quantum key distribution using random quantum states
  publication-title: Quantum Inf. Process.
– volume: 69
  start-page: 2881
  year: 1992
  end-page: 2884
  ident: b11
  article-title: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states
  publication-title: Phys. Rev. Lett.
– volume: 86
  year: 2012
  ident: b22
  article-title: Heralded photon amplification for quantum communication
  publication-title: Phys. Rev. A
– volume: 110
  year: 2013
  ident: b42
  article-title: Universal and optimal error thresholds for measurement-based entanglement purification
  publication-title: Phys. Rev. Lett.
– volume: 70
  start-page: 1895
  year: 1993
  end-page: 1899
  ident: b8
  article-title: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels
  publication-title: Phys. Rev. Lett.
– volume: 67
  start-page: 367
  year: 2022
  end-page: 374
  ident: b18
  article-title: One-step quantum secure direct communication
  publication-title: Sci. Bull.
– volume: 4
  start-page: 1006
  year: 2017
  end-page: 1010
  ident: b73
  article-title: High-dimensional intracity quantum cryptography with structured photons
  publication-title: Optica
– start-page: 83
  year: 2003
  end-page: 120
  ident: b65
  article-title: Decoherence-free subspaces and subsystems
  publication-title: Irreversible Quantum Dynamics
– volume: 67
  year: 2024
  ident: b62
  article-title: Heralded entanglement between error-protected logical qubits for fault-tolerant distributed quantum computing
  publication-title: Sci. China Phys. Mech. Astron.
– volume: 76
  start-page: 722
  year: 1996
  end-page: 725
  ident: b25
  article-title: Purification of noisy entanglement and faithful teleportation via noisy channels
  publication-title: Phys. Rev. Lett.
– volume: 77
  start-page: 2818
  year: 1996
  end-page: 2821
  ident: b28
  article-title: Quantum privacy amplification and the security of quantum cryptography over noisy channels
  publication-title: Phys. Rev. Lett.
– volume: 28
  start-page: 4611
  year: 2020
  end-page: 4624
  ident: b74
  article-title: Efficient quantum key distribution against collective noise using polarization and transverse spatial mode of photons
  publication-title: Opt. Express
– volume: 65
  year: 2002
  ident: b12
  article-title: General scheme for superdense coding between multiparties
  publication-title: Phys. Rev. A
– volume: 89
  year: 2002
  ident: b38
  article-title: Polarization entanglement purification using spatial entanglement
  publication-title: Phys. Rev. Lett.
– volume: 112
  year: 2014
  ident: b60
  article-title: Ultrafast and fault-tolerant quantum communication across long distances
  publication-title: Phys. Rev. Lett.
– volume: 67
  year: 2024
  ident: b63
  article-title: A step toward fault-tolerant distributed quantum computing: Entangling nonlocal logical-qubit with optical quantum multiplexing
  publication-title: Sci. China Phys. Mech. Astron.
– volume: 114
  year: 2015
  ident: b57
  article-title: Nearly deterministic bell measurement for multiphoton qubits and its application to quantum information processing
  publication-title: Phys. Rev. Lett.
– volume: 92
  year: 2020
  ident: b4
  article-title: Secure quantum key distribution with realistic devices
  publication-title: Rev. Modern Phys.
– volume: 98
  year: 2018
  ident: b39
  article-title: Efficient entanglement purification protocols for
  publication-title: Phys. Rev. A
– volume: 71
  year: 2005
  ident: b30
  article-title: Interpolation of recurrence and hashing entanglement distillation protocols
  publication-title: Phys. Rev. A
– volume: 23
  start-page: 9284
  year: 2015
  end-page: 9294
  ident: b35
  article-title: One-step hyperentanglement purification and hyperdistillation with linear optics
  publication-title: Opt. Express
– volume: 376
  start-page: 314
  year: 2012
  end-page: 319
  ident: b46
  article-title: One-step deterministic multipartite entanglement purification with linear optics
  publication-title: Phys. Lett. A
– volume: 65
  year: 2002
  ident: b14
  article-title: Theoretically efficient high-capacity quantum-key-distribution scheme
  publication-title: Phys. Rev. A
– volume: 37
  start-page: 3028
  year: 2020
  end-page: 3033
  ident: b75
  article-title: Free-space quantum secure direct communication based on decoherence-free space
  publication-title: J. Opt. Soc. Am. B
– volume: 74
  start-page: 145
  year: 2002
  end-page: 195
  ident: b3
  article-title: Quantum cryptography
  publication-title: Rev. Modern Phys.
– volume: 22
  start-page: 339
  year: 2023
  ident: b19
  article-title: The hyperentanglement-based quantum secure direct communication protocol with single-photon measurement
  publication-title: Quantum Inf. Process.
– volume: 28
  start-page: 18693
  year: 2020
  end-page: 18706
  ident: b37
  article-title: Imperfect-interaction-free entanglement purification on stationary systems for solid quantum repeaters
  publication-title: Opt. Express
– volume: 68
  start-page: 557
  year: 1992
  end-page: 559
  ident: b2
  article-title: Quantum cryptography without Bell’s theorem
  publication-title: Phys. Rev. Lett.
– volume: 77
  year: 2008
  ident: b32
  article-title: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity
  publication-title: Phys. Rev. A
– volume: 98
  year: 2007
  ident: b70
  article-title: Quantum communication without alignment using multiple-qubit single-photon states
  publication-title: Phys. Rev. Lett.
– volume: 126
  year: 2021
  ident: b54
  article-title: Long-distance entanglement purification for quantum communication
  publication-title: Phys. Rev. Lett.
– volume: 66
  year: 2023
  ident: b24
  article-title: Advances in quantum entanglement purification
  publication-title: Sci. China Phys. Mech. Astron.
– volume: 68
  year: 2003
  ident: b76
  article-title: Transverse-mode beam splitter of a light beam and its application to quantum cryptography
  publication-title: Phys. Rev. A
– volume: 31
  start-page: 15
  year: 2021
  ident: b5
  article-title: Chip-based quantum key distribution
  publication-title: AAPPS Bull.
– volume: 423
  start-page: 417
  year: 2003
  end-page: 422
  ident: b50
  article-title: Experimental entanglement purification of arbitrary unknown states
  publication-title: Nature
– volume: 63
  year: 2001
  ident: b64
  article-title: Theory of decoherence-free fault-tolerant universal quantum computation
  publication-title: Phys. Rev. A
– volume: 21
  start-page: 300
  year: 2022
  ident: b69
  article-title: Purification for hybrid logical qubit entanglement
  publication-title: Quantum Inf. Process.
– volume: 6
  start-page: 28813
  year: 2016
  ident: b66
  article-title: Purification of logic-qubit entanglement
  publication-title: Sci. Rep.
– volume: 70
  start-page: 1381
  year: 2007
  ident: b27
  article-title: Entanglement purification and quantum error correction
  publication-title: Rep. Progr. Phys.
– volume: 6
  start-page: 777
  year: 2012
  end-page: 781
  ident: b59
  article-title: Quantum communication without the necessity of quantum memories
  publication-title: Nat. Photonics
– volume: 66
  year: 2002
  ident: b13
  article-title: Symmetric scheme for superdense coding between multiparties
  publication-title: Phys. Rev. A
– volume: 104
  year: 2021
  ident: b48
  article-title: Entanglement purification by counting and locating errors with entangling measurements
  publication-title: Phys. Rev. A
– volume: 11
  start-page: 695
  year: 2017
  end-page: 699
  ident: b53
  article-title: Experimental nested purification for a linear optical quantum repeater
  publication-title: Nat. Photonics
– volume: 67
  start-page: 661
  year: 1991
  end-page: 663
  ident: b1
  article-title: Quantum cryptography based on Bell’s theorem
  publication-title: Phys. Rev. Lett.
– volume: 81
  year: 2010
  ident: b44
  article-title: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement
  publication-title: Phys. Rev. A
– volume: 109
  year: 2024
  ident: b49
  article-title: Error identification entanglement purification for stationary system using high-dimensional entanglement
  publication-title: Phys. Rev. A
– volume: 443
  start-page: 838
  year: 2006
  end-page: 841
  ident: b51
  article-title: Experimental purification of two-atom entanglement
  publication-title: Nature
– volume: 65
  year: 2022
  ident: b17
  article-title: One-step device-independent quantum secure direct communication
  publication-title: Sci. China Phys. Mech. Astron.
– volume: 127
  year: 2021
  ident: b55
  article-title: Experimental single-copy entanglement distillation
  publication-title: Phys. Rev. Lett.
– volume: 356
  start-page: 928
  year: 2017
  end-page: 932
  ident: b52
  article-title: Entanglement distillation between solid-state quantum network nodes
  publication-title: Science
– volume: 3
  start-page: 961
  year: 2012
  ident: b72
  article-title: Complete experimental toolbox for alignment-free quantum communication
  publication-title: Nat. Commun.
– volume: 90
  year: 2014
  ident: b34
  article-title: Two-step hyperentanglement purification with the quantum-state-joining method
  publication-title: Phys. Rev. A
– volume: 1
  year: 2019
  ident: b10
  article-title: Experimental certification for nonclassical teleportation
  publication-title: Quantum Eng.
– volume: 77
  year: 2008
  ident: b71
  article-title: Quantum key distribution without a shared reference frame
  publication-title: Phys. Rev. A
– volume: 21
  year: 2024
  ident: b23
  article-title: Efficient noiseless linear amplification protocol for single-photon state using imperfect auxiliary photon source
  publication-title: Laser Phys. Lett.
– volume: 105
  year: 2022
  ident: b68
  article-title: Measurement-based logical qubit entanglement purification
  publication-title: Phys. Rev. A
– volume: 25
  start-page: 2969
  year: 2017
  end-page: 2982
  ident: b36
  article-title: Hyperentanglement purification using imperfect spatial entanglement
  publication-title: Opt. Express
– volume: 28
  start-page: 2291
  year: 2020
  end-page: 2301
  ident: b41
  article-title: Purification of the residual entanglement
  publication-title: Opt. Express
– volume: 4
  start-page: 316
  year: 2010
  end-page: 319
  ident: b21
  article-title: Heralded noiseless linear amplification and distillation of entanglement
  publication-title: Nat. Photonics
– volume: 54
  start-page: 3824
  year: 1996
  end-page: 3851
  ident: b26
  article-title: Mixed-state entanglement and quantum error correction
  publication-title: Phys. Rev. A
– volume: 80
  year: 2009
  ident: b33
  article-title: Entanglement purification with double selection
  publication-title: Phys. Rev. A
– volume: 82
  year: 2010
  ident: b45
  article-title: Deterministic polarization-entanglement purification using spatial entanglement
  publication-title: Phys. Rev. A
– volume: 127
  year: 2021
  ident: b47
  article-title: Entanglement-assisted entanglement purification
  publication-title: Phys. Rev. Lett.
– volume: 67
  start-page: 593
  year: 2022
  end-page: 597
  ident: b56
  article-title: Experimental one-step deterministic polarization entanglement purification
  publication-title: Sci. Bull.
– volume: 385
  start-page: 10
  year: 2017
  end-page: 35
  ident: b67
  article-title: Polarization entanglement purification for concatenated Greenberger–Horne–Zeilinger state
  publication-title: Ann. Physics
– volume: 410
  start-page: 1067
  year: 2001
  end-page: 1070
  ident: b29
  article-title: Entanglement purification for quantum communication
  publication-title: Nature
– volume: 535
  year: 2023
  ident: b43
  article-title: Measurement-based hyperentanglement distillation for lossy and distortion photon state
  publication-title: Ann. Phys., Lpz.
– volume: 97
  year: 2018
  ident: b77
  article-title: Experimental investigation of environment-induced entanglement using an all-optical setup
  publication-title: Phys. Rev. A
– volume: 390
  start-page: 575
  year: 1997
  end-page: 579
  ident: b9
  article-title: Experimental quantum teleportation
  publication-title: Nature
– volume: 3
  start-page: 123
  year: 2019
  ident: b40
  article-title: Optimized entanglement purification
  publication-title: Quantum
– volume: 106
  year: 2011
  ident: b58
  article-title: Stable macroscopic quantum superpositions
  publication-title: Phys. Rev. Lett.
– volume: 108
  year: 2023
  ident: b61
  article-title: Hybrid noise protection of logical qubits for universal quantum computation
  publication-title: Phys. Rev. A
– volume: 118
  year: 2017
  ident: b16
  article-title: Quantum secure direct communication with quantum memory
  publication-title: Phys. Rev. Lett.
– volume: 23
  start-page: 304
  year: 2024
  ident: b20
  article-title: Measurement-device-independent multi-party quantum secure direct communication
  publication-title: Quantum Inf. Process.
– volume: 21
  start-page: 300
  issue: 8
  year: 2022
  ident: 10.1016/j.optlastec.2025.112566_b69
  article-title: Purification for hybrid logical qubit entanglement
  publication-title: Quantum Inf. Process.
  doi: 10.1007/s11128-022-03646-y
– volume: 410
  start-page: 1067
  year: 2001
  ident: 10.1016/j.optlastec.2025.112566_b29
  article-title: Entanglement purification for quantum communication
  publication-title: Nature
  doi: 10.1038/35074041
– volume: 77
  start-page: 2818
  year: 1996
  ident: 10.1016/j.optlastec.2025.112566_b28
  article-title: Quantum privacy amplification and the security of quantum cryptography over noisy channels
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.77.2818
– volume: 126
  year: 2021
  ident: 10.1016/j.optlastec.2025.112566_b54
  article-title: Long-distance entanglement purification for quantum communication
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.126.010503
– volume: 67
  start-page: 661
  issue: 6
  year: 1991
  ident: 10.1016/j.optlastec.2025.112566_b1
  article-title: Quantum cryptography based on Bell’s theorem
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.67.661
– volume: 127
  year: 2021
  ident: 10.1016/j.optlastec.2025.112566_b47
  article-title: Entanglement-assisted entanglement purification
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.127.040502
– volume: 76
  start-page: 722
  issue: 5
  year: 1996
  ident: 10.1016/j.optlastec.2025.112566_b25
  article-title: Purification of noisy entanglement and faithful teleportation via noisy channels
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.76.722
– volume: 3
  start-page: 961
  year: 2012
  ident: 10.1016/j.optlastec.2025.112566_b72
  article-title: Complete experimental toolbox for alignment-free quantum communication
  publication-title: Nat. Commun.
  doi: 10.1038/ncomms1951
– volume: 423
  start-page: 417
  issue: 6938
  year: 2003
  ident: 10.1016/j.optlastec.2025.112566_b50
  article-title: Experimental entanglement purification of arbitrary unknown states
  publication-title: Nature
  doi: 10.1038/nature01623
– volume: 70
  start-page: 1895
  year: 1993
  ident: 10.1016/j.optlastec.2025.112566_b8
  article-title: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.70.1895
– volume: 77
  year: 2008
  ident: 10.1016/j.optlastec.2025.112566_b32
  article-title: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity
  publication-title: Phys. Rev. A
– volume: 535
  issue: 4
  year: 2023
  ident: 10.1016/j.optlastec.2025.112566_b43
  article-title: Measurement-based hyperentanglement distillation for lossy and distortion photon state
  publication-title: Ann. Phys., Lpz.
  doi: 10.1002/andp.202200505
– volume: 81
  year: 2010
  ident: 10.1016/j.optlastec.2025.112566_b44
  article-title: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.81.032307
– volume: 82
  year: 2010
  ident: 10.1016/j.optlastec.2025.112566_b45
  article-title: Deterministic polarization-entanglement purification using spatial entanglement
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.82.044304
– volume: 443
  start-page: 838
  issue: 7113
  year: 2006
  ident: 10.1016/j.optlastec.2025.112566_b51
  article-title: Experimental purification of two-atom entanglement
  publication-title: Nature
  doi: 10.1038/nature05146
– volume: 109
  year: 2024
  ident: 10.1016/j.optlastec.2025.112566_b49
  article-title: Error identification entanglement purification for stationary system using high-dimensional entanglement
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.109.042423
– volume: 37
  start-page: 3028
  issue: 10
  year: 2020
  ident: 10.1016/j.optlastec.2025.112566_b75
  article-title: Free-space quantum secure direct communication based on decoherence-free space
  publication-title: J. Opt. Soc. Am. B
  doi: 10.1364/JOSAB.397973
– volume: 28
  start-page: 18693
  issue: 13
  year: 2020
  ident: 10.1016/j.optlastec.2025.112566_b37
  article-title: Imperfect-interaction-free entanglement purification on stationary systems for solid quantum repeaters
  publication-title: Opt. Express
  doi: 10.1364/OE.394617
– volume: 118
  year: 2017
  ident: 10.1016/j.optlastec.2025.112566_b16
  article-title: Quantum secure direct communication with quantum memory
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.118.220501
– volume: 80
  year: 2009
  ident: 10.1016/j.optlastec.2025.112566_b33
  article-title: Entanglement purification with double selection
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.80.042308
– volume: 66
  year: 2002
  ident: 10.1016/j.optlastec.2025.112566_b13
  article-title: Symmetric scheme for superdense coding between multiparties
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.66.014301
– volume: 65
  issue: 3
  year: 2002
  ident: 10.1016/j.optlastec.2025.112566_b14
  article-title: Theoretically efficient high-capacity quantum-key-distribution scheme
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.65.032302
– volume: 6
  start-page: 777
  issue: 11
  year: 2012
  ident: 10.1016/j.optlastec.2025.112566_b59
  article-title: Quantum communication without the necessity of quantum memories
  publication-title: Nat. Photonics
  doi: 10.1038/nphoton.2012.243
– volume: 92
  year: 2020
  ident: 10.1016/j.optlastec.2025.112566_b4
  article-title: Secure quantum key distribution with realistic devices
  publication-title: Rev. Modern Phys.
  doi: 10.1103/RevModPhys.92.025002
– volume: 67
  year: 2024
  ident: 10.1016/j.optlastec.2025.112566_b62
  article-title: Heralded entanglement between error-protected logical qubits for fault-tolerant distributed quantum computing
  publication-title: Sci. China Phys. Mech. Astron.
  doi: 10.1007/s11433-023-2245-9
– volume: 385
  start-page: 10
  year: 2017
  ident: 10.1016/j.optlastec.2025.112566_b67
  article-title: Polarization entanglement purification for concatenated Greenberger–Horne–Zeilinger state
  publication-title: Ann. Physics
  doi: 10.1016/j.aop.2017.07.012
– volume: 23
  start-page: 9284
  issue: 7
  year: 2015
  ident: 10.1016/j.optlastec.2025.112566_b35
  article-title: One-step hyperentanglement purification and hyperdistillation with linear optics
  publication-title: Opt. Express
  doi: 10.1364/OE.23.009284
– volume: 356
  start-page: 928
  issue: 6341
  year: 2017
  ident: 10.1016/j.optlastec.2025.112566_b52
  article-title: Entanglement distillation between solid-state quantum network nodes
  publication-title: Science
  doi: 10.1126/science.aan0070
– volume: 97
  year: 2018
  ident: 10.1016/j.optlastec.2025.112566_b77
  article-title: Experimental investigation of environment-induced entanglement using an all-optical setup
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.97.022321
– volume: 22
  start-page: 109
  year: 2023
  ident: 10.1016/j.optlastec.2025.112566_b6
  article-title: Device-independent quantum key distribution using random quantum states
  publication-title: Quantum Inf. Process.
  doi: 10.1007/s11128-023-03852-2
– volume: 106
  year: 2011
  ident: 10.1016/j.optlastec.2025.112566_b58
  article-title: Stable macroscopic quantum superpositions
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.106.110402
– volume: 89
  issue: 25
  year: 2002
  ident: 10.1016/j.optlastec.2025.112566_b38
  article-title: Polarization entanglement purification using spatial entanglement
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.89.257901
– volume: 1
  issue: 2
  year: 2019
  ident: 10.1016/j.optlastec.2025.112566_b10
  article-title: Experimental certification for nonclassical teleportation
  publication-title: Quantum Eng.
  doi: 10.1002/que2.13
– volume: 67
  start-page: 593
  issue: 6
  year: 2022
  ident: 10.1016/j.optlastec.2025.112566_b56
  article-title: Experimental one-step deterministic polarization entanglement purification
  publication-title: Sci. Bull.
  doi: 10.1016/j.scib.2021.12.018
– volume: 108
  year: 2023
  ident: 10.1016/j.optlastec.2025.112566_b61
  article-title: Hybrid noise protection of logical qubits for universal quantum computation
  publication-title: Phys. Rev. A
– volume: 69
  start-page: 2881
  year: 1992
  ident: 10.1016/j.optlastec.2025.112566_b11
  article-title: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.69.2881
– volume: 11
  start-page: 695
  issue: 11
  year: 2017
  ident: 10.1016/j.optlastec.2025.112566_b53
  article-title: Experimental nested purification for a linear optical quantum repeater
  publication-title: Nat. Photonics
  doi: 10.1038/s41566-017-0010-6
– volume: 28
  start-page: 4611
  issue: 4
  year: 2020
  ident: 10.1016/j.optlastec.2025.112566_b74
  article-title: Efficient quantum key distribution against collective noise using polarization and transverse spatial mode of photons
  publication-title: Opt. Express
  doi: 10.1364/OE.374292
– volume: 114
  year: 2015
  ident: 10.1016/j.optlastec.2025.112566_b57
  article-title: Nearly deterministic bell measurement for multiphoton qubits and its application to quantum information processing
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.114.113603
– volume: 110
  year: 2013
  ident: 10.1016/j.optlastec.2025.112566_b42
  article-title: Universal and optimal error thresholds for measurement-based entanglement purification
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.110.260503
– volume: 70
  start-page: 1381
  issue: 8
  year: 2007
  ident: 10.1016/j.optlastec.2025.112566_b27
  article-title: Entanglement purification and quantum error correction
  publication-title: Rep. Progr. Phys.
  doi: 10.1088/0034-4885/70/8/R03
– volume: 112
  year: 2014
  ident: 10.1016/j.optlastec.2025.112566_b60
  article-title: Ultrafast and fault-tolerant quantum communication across long distances
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.112.250501
– volume: 104
  year: 2021
  ident: 10.1016/j.optlastec.2025.112566_b48
  article-title: Entanglement purification by counting and locating errors with entangling measurements
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.104.012419
– volume: 31
  start-page: 15
  year: 2021
  ident: 10.1016/j.optlastec.2025.112566_b5
  article-title: Chip-based quantum key distribution
  publication-title: AAPPS Bull.
  doi: 10.1007/s43673-021-00017-0
– volume: 22
  start-page: 339
  year: 2023
  ident: 10.1016/j.optlastec.2025.112566_b19
  article-title: The hyperentanglement-based quantum secure direct communication protocol with single-photon measurement
  publication-title: Quantum Inf. Process.
  doi: 10.1007/s11128-023-04097-9
– volume: 86
  year: 2012
  ident: 10.1016/j.optlastec.2025.112566_b22
  article-title: Heralded photon amplification for quantum communication
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.86.023815
– volume: 77
  issue: 3
  year: 2008
  ident: 10.1016/j.optlastec.2025.112566_b71
  article-title: Quantum key distribution without a shared reference frame
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.77.032345
– volume: 65
  year: 2002
  ident: 10.1016/j.optlastec.2025.112566_b12
  article-title: General scheme for superdense coding between multiparties
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.65.022304
– volume: 3
  start-page: 123
  year: 2019
  ident: 10.1016/j.optlastec.2025.112566_b40
  article-title: Optimized entanglement purification
  publication-title: Quantum
  doi: 10.22331/q-2019-02-18-123
– volume: 63
  year: 2001
  ident: 10.1016/j.optlastec.2025.112566_b64
  article-title: Theory of decoherence-free fault-tolerant universal quantum computation
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.63.042307
– volume: 25
  start-page: 2969
  issue: 3
  year: 2017
  ident: 10.1016/j.optlastec.2025.112566_b36
  article-title: Hyperentanglement purification using imperfect spatial entanglement
  publication-title: Opt. Express
  doi: 10.1364/OE.25.002969
– volume: 6
  start-page: 28813
  year: 2016
  ident: 10.1016/j.optlastec.2025.112566_b66
  article-title: Purification of logic-qubit entanglement
  publication-title: Sci. Rep.
  doi: 10.1038/srep28813
– volume: 105
  year: 2022
  ident: 10.1016/j.optlastec.2025.112566_b68
  article-title: Measurement-based logical qubit entanglement purification
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.105.062418
– volume: 68
  start-page: 557
  year: 1992
  ident: 10.1016/j.optlastec.2025.112566_b2
  article-title: Quantum cryptography without Bell’s theorem
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.68.557
– volume: 98
  year: 2018
  ident: 10.1016/j.optlastec.2025.112566_b39
  article-title: Efficient entanglement purification protocols for d-level systems
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.98.042309
– volume: 68
  year: 2003
  ident: 10.1016/j.optlastec.2025.112566_b76
  article-title: Transverse-mode beam splitter of a light beam and its application to quantum cryptography
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.68.012323
– volume: 21
  issue: 2
  year: 2024
  ident: 10.1016/j.optlastec.2025.112566_b23
  article-title: Efficient noiseless linear amplification protocol for single-photon state using imperfect auxiliary photon source
  publication-title: Laser Phys. Lett.
  doi: 10.1088/1612-202X/ad1aaa
– volume: 72
  year: 2005
  ident: 10.1016/j.optlastec.2025.112566_b31
  article-title: Entanglement distillation protocols and number theory
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.72.032313
– volume: 98
  issue: 10
  year: 2007
  ident: 10.1016/j.optlastec.2025.112566_b70
  article-title: Quantum communication without alignment using multiple-qubit single-photon states
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.98.100501
– volume: 4
  start-page: 316
  year: 2010
  ident: 10.1016/j.optlastec.2025.112566_b21
  article-title: Heralded noiseless linear amplification and distillation of entanglement
  publication-title: Nat. Photonics
  doi: 10.1038/nphoton.2010.35
– volume: 23
  start-page: 304
  year: 2024
  ident: 10.1016/j.optlastec.2025.112566_b20
  article-title: Measurement-device-independent multi-party quantum secure direct communication
  publication-title: Quantum Inf. Process.
  doi: 10.1007/s11128-024-04505-8
– volume: 54
  start-page: 3824
  year: 1996
  ident: 10.1016/j.optlastec.2025.112566_b26
  article-title: Mixed-state entanglement and quantum error correction
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.54.3824
– volume: 67
  year: 2024
  ident: 10.1016/j.optlastec.2025.112566_b63
  article-title: A step toward fault-tolerant distributed quantum computing: Entangling nonlocal logical-qubit with optical quantum multiplexing
  publication-title: Sci. China Phys. Mech. Astron.
  doi: 10.1007/s11433-023-2258-x
– volume: 74
  start-page: 145
  year: 2002
  ident: 10.1016/j.optlastec.2025.112566_b3
  article-title: Quantum cryptography
  publication-title: Rev. Modern Phys.
  doi: 10.1103/RevModPhys.74.145
– volume: 23
  start-page: 64
  year: 2024
  ident: 10.1016/j.optlastec.2025.112566_b7
  article-title: A hybrid dynamic n-party quantum key exchange protocol based on three-particle GHZ states
  publication-title: Quantum Inf. Process.
  doi: 10.1007/s11128-024-04271-7
– volume: 376
  start-page: 314
  issue: 4
  year: 2012
  ident: 10.1016/j.optlastec.2025.112566_b46
  article-title: One-step deterministic multipartite entanglement purification with linear optics
  publication-title: Phys. Lett. A
  doi: 10.1016/j.physleta.2011.09.056
– volume: 66
  year: 2023
  ident: 10.1016/j.optlastec.2025.112566_b24
  article-title: Advances in quantum entanglement purification
  publication-title: Sci. China Phys. Mech. Astron.
  doi: 10.1007/s11433-022-2065-x
– volume: 65
  year: 2022
  ident: 10.1016/j.optlastec.2025.112566_b17
  article-title: One-step device-independent quantum secure direct communication
  publication-title: Sci. China Phys. Mech. Astron.
  doi: 10.1007/s11433-021-1863-9
– volume: 390
  start-page: 575
  year: 1997
  ident: 10.1016/j.optlastec.2025.112566_b9
  article-title: Experimental quantum teleportation
  publication-title: Nature
  doi: 10.1038/37539
– volume: 90
  year: 2014
  ident: 10.1016/j.optlastec.2025.112566_b34
  article-title: Two-step hyperentanglement purification with the quantum-state-joining method
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.90.052309
– volume: 4
  start-page: 1006
  issue: 9
  year: 2017
  ident: 10.1016/j.optlastec.2025.112566_b73
  article-title: High-dimensional intracity quantum cryptography with structured photons
  publication-title: Optica
  doi: 10.1364/OPTICA.4.001006
– volume: 71
  year: 2005
  ident: 10.1016/j.optlastec.2025.112566_b30
  article-title: Interpolation of recurrence and hashing entanglement distillation protocols
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.71.062325
– start-page: 83
  year: 2003
  ident: 10.1016/j.optlastec.2025.112566_b65
  article-title: Decoherence-free subspaces and subsystems
– volume: 68
  issue: 4
  year: 2003
  ident: 10.1016/j.optlastec.2025.112566_b15
  article-title: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.68.042317
– volume: 67
  start-page: 367
  issn: 2095-9273
  issue: 4
  year: 2022
  ident: 10.1016/j.optlastec.2025.112566_b18
  article-title: One-step quantum secure direct communication
  publication-title: Sci. Bull.
  doi: 10.1016/j.scib.2021.11.002
– volume: 127
  year: 2021
  ident: 10.1016/j.optlastec.2025.112566_b55
  article-title: Experimental single-copy entanglement distillation
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.127.040506
– volume: 28
  start-page: 2291
  issue: 2
  year: 2020
  ident: 10.1016/j.optlastec.2025.112566_b41
  article-title: Purification of the residual entanglement
  publication-title: Opt. Express
  doi: 10.1364/OE.383499
SSID ssj0004653
Score 2.400877
Snippet We propose two types of logical qubit entanglement purification protocols (LEPPs) to reduce the effect of noises inside and outside the logical qubit subspace...
SourceID crossref
elsevier
SourceType Index Database
Publisher
StartPage 112566
SubjectTerms Entanglement purification
Error correction
Linear optics
Logical qubit
Title Polarization-transverse-spatial logical qubit entanglement purification using linear optics
URI https://dx.doi.org/10.1016/j.optlastec.2025.112566
Volume 185
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PS8MwFH6MiaAH0ak4f4wcvMa1adM5b0McU3F4cDDwUJI0HfPQ1a27-rf7XpvKBoIHjy1JCF_Ce1-a730FuBZhlBqpI7pu7HG6v-VaJ4KHmFuQJclElp-yX8bRaBI-TeW0Afd1LQzJKl3sr2J6Ga3dm65Ds5vP51Tji-GXbFVlZTRGFexhj3b5zZe_URvpnCgDjDfYekvjtcgL5KiFJS9DIamcRpZ2ib9kqI2sMzyEA0cX2aCa0RE0bNaC_Q0TwRbsliJOszqG91c6p7rCSl5QFiLRheUrkk3jMC7Osc-1nheMVOPZrJKPs3y9JNFQ2ZWRGH7GiICqJcPZ4-gnMBk-vN2PuPt5Ajd4BCu4UFIHNhR-GkR-iixD9IX2la88bXsJEgudBniYEoHxTT-RKrRap8oIZYVHmS04hWa2yOwZMB9JEwLsWethM6Qs2kQmQl5469u-krYNXg1YnFceGXEtHvuIfzCOCeO4wrgNdzWw8dZyxxjJ_-p8_p_OF7BHT5Xi9hKaxXJtr5BXFLpTbpwO7Awen0fjb8pLzt4
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1NS8NAEB1qRdSDaFWsn3vQY2yyyaZW8CBqae0HHlooeIjZdFPqoY1tinjxT_kHnUk20oLgQXpNssvydnnzNvtmFuCcO24YCOnScWPZoPNbQ8o-NxyMLaiSRF8kv7JbbbfWdR57opeDrywXhmyVmvtTTk_YWj8paTRL0XBIOb5Iv1RWVaSFxrSzsqE-3nHfNr2p3-MkX3Befejc1Qx9tYAR4AYlNrgvpK0cboW2a4UYg3mFS8u3fFOqch_Drgxt3GpwO7CCSl_4jpIy9APuK24S79vY7wqsOkgXdG3C5ac1l4ypS1_aSHA4vAVT2TiKURTHioonckH5OyKpz_hLSJwLc9Vt2NL6lN2mEOxATo0KsDlXtbAAa4lrNJjuwvMTbYx1JqcRU9gjl4cypuTTxm40sbK3mRzGjGzqo0HqV2fRbEIupaQpI_f9gJHi9ScMR4-970F3KZDuQ340HqkDYBaqNJxRUykTP0ONJAM3cFGIXlmq4gtVBDMDzIvSohxe5lZ79X4w9ghjL8W4CNcZsN7C-vIwdPzV-PA_jc9gvdZpNb1mvd04gg16k9p9jyEfT2bqBEVNLE-TRcTgZdmr9hua5gpB
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Polarization-transverse-spatial+logical+qubit+entanglement+purification+using+linear+optics&rft.jtitle=Optics+and+laser+technology&rft.au=Guo%2C+Peng-Liang&rft.au=Gao%2C+Cheng-Yan&rft.au=Ren%2C+Bao-Cang&rft.date=2025-07-01&rft.issn=0030-3992&rft.volume=185&rft.spage=112566&rft_id=info:doi/10.1016%2Fj.optlastec.2025.112566&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_optlastec_2025_112566
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0030-3992&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0030-3992&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0030-3992&client=summon