Unitarity Estimation for Quantum Channels

Chen, K; Wang, Q; Long, P; Ying, M

Unitarity Estimation for Quantum Channels

Chen, K Wang, Q Long, P Ying, M

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2023, 69, (8), pp. 5116-5134
Issue Date:: 2023-08-01

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Field	Value	Language
dc.contributor.author	Chen, K
dc.contributor.author	Wang, Q
dc.contributor.author	Long, P
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X
dc.date.accessioned	2024-03-06T05:05:14Z
dc.date.available	2024-03-06T05:05:14Z
dc.date.issued	2023-08-01
dc.identifier.citation	IEEE Transactions on Information Theory, 2023, 69, (8), pp. 5116-5134
dc.identifier.issn	0018-9448
dc.identifier.issn	1557-9654
dc.identifier.uri	http://hdl.handle.net/10453/176200
dc.description.abstract	Estimating the unitarity of an unknown quantum channel E provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be performed with either coherent or incoherent access, where the former in general leads to better query complexity while the latter allows more practical implementations. In this paper, we provide a unified framework for unitarity estimation, which induces ancilla-efficient algorithms that use O(ϵ-2) and O(√d · ϵ-2) calls to E with coherent and incoherent accesses, respectively, where d is the dimension of the system that E acts on and ϵ is the required precision. We further show that both the d-dependence and ϵ -dependence of our algorithms are optimal. As part of our results, we settle the query complexity of the distinguishing problem for depolarizing and unitary channels with incoherent access by giving a matching lower bound Ω (√d) , improving the prior best lower bound Ω (3√d) by (Aharonov et al., 2022) and (Chen et al., FOCS 2021).
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation	National Natural Science Foundation of China61832015
dc.relation.ispartof	IEEE Transactions on Information Theory
dc.relation.isbasedon	10.1109/TIT.2023.3263645
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.subject.classification	4006 Communications engineering
dc.subject.classification	4613 Theory of computation
dc.title	Unitarity Estimation for Quantum Channels
dc.type	Journal Article
utslib.citation.volume	69
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	1005 Communications Technologies
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	closed_access	*
dc.date.updated	2024-03-06T05:05:13Z
pubs.issue	8
pubs.publication-status	Published
pubs.volume	69
utslib.citation.issue	8

Abstract:

Estimating the unitarity of an unknown quantum channel E provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be performed with either coherent or incoherent access, where the former in general leads to better query complexity while the latter allows more practical implementations. In this paper, we provide a unified framework for unitarity estimation, which induces ancilla-efficient algorithms that use O(ϵ-2) and O(√d · ϵ-2) calls to E with coherent and incoherent accesses, respectively, where d is the dimension of the system that E acts on and ϵ is the required precision. We further show that both the d-dependence and ϵ -dependence of our algorithms are optimal. As part of our results, we settle the query complexity of the distinguishing problem for depolarizing and unitary channels with incoherent access by giving a matching lower bound Ω (√d) , improving the prior best lower bound Ω (3√d) by (Aharonov et al., 2022) and (Chen et al., FOCS 2021).

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http://hdl.handle.net/10453/176200