An Efficient Parameterized Algorithm for Computing Quantum Channel Fidelity via Symmetries Exploitation

Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021] introduced an asymptotically converging semidefinite programmi...

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Published in:IEEE transactions on information theory Vol. 71; no. 9; pp. 7003 - 7015
Main Authors: Chee, Yeow Meng, Ta, Hoang, Vu, Van Khu
Format: Journal Article
Language:English
Published: IEEE 01.09.2025
Subjects:
bilinear optimization
Data mining
de Finetti theorems
Hilbert space
Matrix converters
Noise measurement
Optimization
Polynomials
Quantum channels
Quantum entanglement
Quantum error correction
Quantum mechanics
semidefinite programming
Symmetric matrices
ISSN:0018-9448, 1557-9654
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Abstract Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021] introduced an asymptotically converging semidefinite programming hierarchy of outer bounds for this quantity. However, the size of the semidefinite programs (SDPs) grows exponentially with respect to the level of the hierarchy, thus making their computation unscalable. In this work, by exploiting the symmetries in the SDP, we show that, for a fixed output dimension of the quantum channel, we can compute the SDP in time polynomial with respect to the level of the hierarchy and input dimension. As a direct consequence of our result, the optimal fidelity can be approximated with an accuracy of <inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula> in <inline-formula> <tex-math notation="LaTeX">\mathrm {poly}(1/\epsilon, \text {input dimension}) </tex-math></inline-formula> time, compared to the <inline-formula> <tex-math notation="LaTeX">\exp (1/\epsilon, \text {input dimension}) </tex-math></inline-formula> running time required for direct computation.
AbstractList Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021] introduced an asymptotically converging semidefinite programming hierarchy of outer bounds for this quantity. However, the size of the semidefinite programs (SDPs) grows exponentially with respect to the level of the hierarchy, thus making their computation unscalable. In this work, by exploiting the symmetries in the SDP, we show that, for a fixed output dimension of the quantum channel, we can compute the SDP in time polynomial with respect to the level of the hierarchy and input dimension. As a direct consequence of our result, the optimal fidelity can be approximated with an accuracy of <inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula> in <inline-formula> <tex-math notation="LaTeX">\mathrm {poly}(1/\epsilon, \text {input dimension}) </tex-math></inline-formula> time, compared to the <inline-formula> <tex-math notation="LaTeX">\exp (1/\epsilon, \text {input dimension}) </tex-math></inline-formula> running time required for direct computation.
Author Chee, Yeow Meng
Ta, Hoang
Vu, Van Khu
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Cites_doi 10.1137/15M1037731
10.1038/s41534-025-00980-8
10.1017/CBO9781107447226
10.1007/s10107-006-0039-7
10.1109/TIT.2009.2039162
10.1038/ncomms11419
10.1137/21M1413298
10.1016/j.disc.2019.05.019
10.1137/20M1369592
10.1109/TIT.2005.851748
10.1109/TIT.2018.2874031
10.1007/s11081-008-9050-6
10.1103/PhysRevA.75.012338
10.1002/j.1538-7305.1948.tb01338.x
10.22331/q-2024-04-30-1318
10.1007/s10623-016-0216-5
10.1109/ISIT.2016.7541587
10.1016/j.jcta.2006.03.010
10.1090/s0273-0979-08-01201-9
10.1007/s00220-007-0189-3
10.1007/s10107-006-0030-3
10.1103/PhysRevLett.94.080501
10.1007/978-1-4684-9458-7
10.1109/TIT.2009.2030478
10.1109/TIT.2024.3410047
10.1103/physreva.107.012428
10.1016/j.jpaa.2003.12.011
10.1109/TIT.2024.3355929
10.1007/s10107-023-02028-1
10.1109/TIT.2023.3301719
10.1109/TIT.2022.3182101
10.1007/s10107-021-01650-1
10.1109/ISIT.2019.8849617
10.1103/PhysRevA.104.022401
10.1007/s10107-021-01677-4
10.1103/PhysRevLett.88.187904
10.1109/TIT.2015.2439953
10.1287/moor.1120.0558
10.1007/s10107-017-1127-6
10.1103/PhysRevA.69.022308
10.1016/j.ejor.2009.01.025
10.1103/PhysRevLett.123.070502
10.1109/TIT.2017.2696963
10.1016/j.laa.2008.07.025
10.1109/TIT.2010.2043769
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References ref12
ref15
ref14
ref52
ref11
ref10
Fulton (ref51) 2013; 129
Gijswijt (ref53) 2009
ref17
ref16
ref19
ref18
ref50
ref48
ref47
ref42
Huber (ref43) 2022
ref41
ref44
Gharibian (ref46) 2010; 10
ref49
ref8
ref7
ref9
ref4
ref3
ref6
ref5
ref40
ref35
ref34
Polak (ref20) 2019
ref37
ref36
ref31
ref30
ref33
ref32
Lasserre (ref24) 2011
ref2
ref1
ref39
ref38
Johnson (ref13) 2017
ref23
ref26
ref25
ref22
ref21
ref28
ref27
ref29
Francesco (ref45) 2022
References_xml – ident: ref5
  doi: 10.1137/15M1037731
– ident: ref44
  doi: 10.1038/s41534-025-00980-8
– ident: ref49
  doi: 10.1017/CBO9781107447226
– ident: ref36
  doi: 10.1007/s10107-006-0039-7
– ident: ref12
  doi: 10.1109/TIT.2009.2039162
– ident: ref14
  doi: 10.1038/ncomms11419
– ident: ref35
  doi: 10.1137/21M1413298
– ident: ref33
  doi: 10.1016/j.disc.2019.05.019
– ident: ref34
  doi: 10.1137/20M1369592
– year: 2022
  ident: ref45
  article-title: De Finetti methods in quantum information
– ident: ref30
  doi: 10.1109/TIT.2005.851748
– ident: ref16
  doi: 10.1109/TIT.2018.2874031
– ident: ref38
  doi: 10.1007/s11081-008-9050-6
– ident: ref11
  doi: 10.1103/PhysRevA.75.012338
– ident: ref1
  doi: 10.1002/j.1538-7305.1948.tb01338.x
– ident: ref27
  doi: 10.22331/q-2024-04-30-1318
– ident: ref19
  doi: 10.1007/s10623-016-0216-5
– volume: 10
  start-page: 343
  issue: 3
  year: 2010
  ident: ref46
  article-title: Strong NP-hardness of the quantum separability problem
  publication-title: Quantum Inf. Comput.
– volume: 129
  volume-title: Representation Theory: A First Course
  year: 2013
  ident: ref51
– volume-title: Handbook on Semidefinite, Conic and Polynomial Optimization
  year: 2011
  ident: ref24
– ident: ref15
  doi: 10.1109/ISIT.2016.7541587
– ident: ref31
  doi: 10.1016/j.jcta.2006.03.010
– ident: ref52
  doi: 10.1090/s0273-0979-08-01201-9
– ident: ref48
  doi: 10.1007/s00220-007-0189-3
– ident: ref32
  doi: 10.1007/s10107-006-0030-3
– ident: ref10
  doi: 10.1103/PhysRevLett.94.080501
– ident: ref50
  doi: 10.1007/978-1-4684-9458-7
– ident: ref3
  doi: 10.1109/TIT.2009.2030478
– ident: ref8
  doi: 10.1109/TIT.2024.3410047
– ident: ref23
  doi: 10.1103/physreva.107.012428
– ident: ref39
  doi: 10.1016/j.jpaa.2003.12.011
– year: 2009
  ident: ref53
  article-title: Block diagonalization for algebra’s associated with block codes
  publication-title: arXiv:0910.4515
– ident: ref42
  doi: 10.1109/TIT.2024.3355929
– ident: ref37
  doi: 10.1007/s10107-023-02028-1
– ident: ref21
  doi: 10.1109/TIT.2023.3301719
– ident: ref28
  doi: 10.1109/TIT.2022.3182101
– ident: ref18
  doi: 10.1007/s10107-021-01650-1
– ident: ref6
  doi: 10.1109/ISIT.2019.8849617
– ident: ref22
  doi: 10.1103/PhysRevA.104.022401
– ident: ref7
  doi: 10.1007/s10107-021-01677-4
– year: 2022
  ident: ref43
  article-title: Refuting spectral compatibility of quantum marginals
  publication-title: arXiv:2211.06349
– ident: ref47
  doi: 10.1103/PhysRevLett.88.187904
– ident: ref9
  doi: 10.1109/TIT.2015.2439953
– ident: ref40
  doi: 10.1287/moor.1120.0558
– ident: ref41
  doi: 10.1007/s10107-017-1127-6
– ident: ref29
  doi: 10.1103/PhysRevA.69.022308
– ident: ref26
  doi: 10.1016/j.ejor.2009.01.025
– year: 2019
  ident: ref20
  article-title: New methods in coding theory: Error-correcting codes and the Shannon capacity
– year: 2017
  ident: ref13
  article-title: QVECTOR: An algorithm for device-tailored quantum error correction
  publication-title: arXiv:1711.02249
– ident: ref17
  doi: 10.1103/PhysRevLett.123.070502
– ident: ref2
  doi: 10.1109/TIT.2017.2696963
– ident: ref25
  doi: 10.1016/j.laa.2008.07.025
– ident: ref4
  doi: 10.1109/TIT.2010.2043769
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Snippet Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information...
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SubjectTerms bilinear optimization
Data mining
de Finetti theorems
Hilbert space
Matrix converters
Noise measurement
Optimization
Polynomials
Quantum channels
Quantum entanglement
Quantum error correction
Quantum mechanics
semidefinite programming
Symmetric matrices
Title An Efficient Parameterized Algorithm for Computing Quantum Channel Fidelity via Symmetries Exploitation
URI https://ieeexplore.ieee.org/document/11082348
Volume 71
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