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Cited by 5Quantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

Estimation of correlations and nonseparability in quantum channels via unitarity benchmarking

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Girling, Matthew, Cîrstoiu, Cristina, Jennings, David·2022·Physical Review Research
DOI 10.1103/physrevresearch.4.023041
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Abstract

The ability to transfer quantum information between systems is a fundamental component of quantum technologies and leads to correlations within the global quantum process. However, correlation structures in quantum channels are less studied than those in quantum states. Motivated by recent techniques in randomized benchmarking, we develop a range of results for efficient estimation of correlations within a bipartite quantum channel. We introduce subunitarity measures that are invariant under local changes of basis, generalize the unitarity of a channel, and allow for the analysis of quantum information exchange within channels. Using these, we show that unitarity is monogamous, and we provide an information-disturbance relation. We then define a notion of correlated unitarity that quantifies the correlations within a given channel. Crucially, we show that this measure is strictly bounded on the set of separable channels and therefore provides a witness of nonseparability. Finally, we describe how such measures for effective noise channels can be efficiently estimated within different randomized benchmarking protocols. We find that the correlated unitarity can be estimated in a SPAM-robust manner for any separable quantum channel, and we show that a benchmarking/tomography protocol with mid-circuit resets can reliably witness nonseparability for sufficiently small reset errors. The tools we develop provide information beyond that obtained via simultaneous randomized benchmarking and so could find application in the analysis of cross-talk errors in quantum devices.

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  • For any quantum channel F, the unital block T_F is a real matrix.

    “For any quantum channel F, the unital block T F is real matrix [83], therefore 2 , where λ k (F ) denote eigenvalues and σ k (F ) singular values of T F .”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [83]

    In “Proof of u_c as a witness of nonseparability” (Eq. C25; page unavailable), the paper expresses the T-matrix of a qubit channel using real diagonal entries and orthogonal matrices. But “The Liouville representation of quantum channels” defines T using an orthonormal operator basis without requiring that basis to be Hermitian, so our copy does not establish that T is real for every quantum channel in that representation. (LLM, conf=0.83)

    Experimental — accuracy not yet measured

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Cited by

Sorted by citations

Authors
Girling, M., Cîrstoiu, C., & Jennings, D.
Affiliations
University of Leeds (GB)
ORCID
Venue
Physical Review Research
Publisher
American Physical Society (APS)
Published
2022-04-15
Volume
4
Issue
2
ISSN
2643-1564 (ISSN-L)
DOI
10.1103/physrevresearch.4.023041
OpenAlex
W3161328668
Cited by
5
References
11
Citations by year
2025: 1 · 2024: 1 · 2023: 3
FWCI
0.41
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review Research (publishedVersion, cc-by)
  • White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (acceptedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • Spiral (Imperial College London) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
Royal Society
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum channels, quantum correlations, non-separability

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