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Composed ensembles of random unitary matrices
Open accessAbstract
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate their physical relevance. We also discuss the methods of generating random matrices distributed according to invariant Haar measure on the orthogonal and unitary group.
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“The key idea is to choose the target transformation U randomly from the Haar measure [12]. This will earn us the advantage of the concentration of measure in large Hilbert spaces, as described further below, and leads to a universal form of the gate fidelity depending only on the intrinsic strength of the cumulative noise.”
From Scalable noise estimation with random unitary operators (2005) · cites this paper as [12]
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“The only inefficiency of our protocol is the requirement of experimentally implementing a Haar-random unitary: the decomposition into elementary one and two qubit gates requires an exponentially long gate sequence [12].”
From Scalable noise estimation with random unitary operators (2005) · cites this paper as [12]
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Cites
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Cited by
Sorted by citations
Volume of the set of separable states
Życzkowski, K., Horodecki, P., Sanpera, A., & Lewenstein, M. (1998) · Physical Review A · doi:10.1103/physreva.58.883 · Cited by 1,411
Scalable noise estimation with random unitary operators
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Self-citationInduced measures in the space of mixed quantum states
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Entanglement and the power of one qubit
Datta, A., Flammia, S. T., & Caves, C. M. (2005) · Physical Review A · doi:10.1103/physreva.72.042316 · Cited by 372
Dynamics of quantum entanglement
Życzkowski, K., Horodecki, P., Horodecki, M., & Horodecki, R. (2001) · Physical Review A · doi:10.1103/physreva.65.012101 · Cited by 362
Metadata
- Authors
- Pozniak, M., Zyczkowski, K., & Kus, M.
- Affiliations
- Jagiellonian University (PL)
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1998-01-23
- Volume
- 31
- Issue
- 3
- Pages
- 1059-1071
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1993950005
- Cited by
- 128
- References
- 26
- Citations by year
- 2025: 3 · 2024: 4 · 2023: 4 · 2022: 1 · 2021: 2 · 2020: 4 · 2019: 1 · 2018: 5 · 2017: 2 · 2016: 3 · 2015: 6 · 2014: 5 · 2013: 6 · 2012: 2
- FWCI
- 8.51
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- random unitary matrices, matrix products, eigenvalue statistics, Haar measure, unitary groups, orthogonal group, random matrix theory
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