Unitary quantum gates, perfect entanglers, and unistochastic maps
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Nonlocal properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix $U$ equal to the Shannon entropy of the vector of singular values of the reshuffled matrix. Averaging the entropy over the Haar measure on $U({N}^{2})$ we find its asymptotic behavior. For two-qubit quantum gates we derive the induced probability distribution of the interaction content and show that the relative volume of the set of perfect entanglers reads $8/3\ensuremath{\pi}\ensuremath{\approx}0.85$. We establish explicit conditions under which a given one-qubit bistochastic map is unistochastic, so it can be obtained by partial trace over a one-qubit environment initially prepared in the maximally mixed state.
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Multi-qubit experiments are susceptible to larger error rates than isolated two-qubit gates, due to correlated errors across many ions.
“However, multi-qubit experiments are susceptible to larger error rates than isolated two-qubit gates, due to correlated errors across many ions [35].”
From Validating quantum computers using randomized model circuits (2019) · cites this paper as [35]
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Goerz, M. H., Basilewitsch, D., Gago-Encinas, F., et al. (2019) · SciPost Physics · doi:10.21468/scipost.report.1237
(2019) · SciPost Physics · doi:10.21468/scipost.report.1228
Nonlocal characteristics of two-qubit gates from Argand diagram geometry
Selvan, M. K., & Balakrishnan, S. (2026) · Physica Scripta · doi:10.1088/1402-4896/ae2dd4
Quantum circuit theory by unitary operators derived from Kaniadakis κ-generalization
Freitas, A. J. S., & da Silva, J. L. E. (2025) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-025-06440-8
Experimental Observation of Dynamical Phase Transitions in a Dephased Photonic Quantum Walk
Anonymous, Xiao, L., Huo, B., Wang, X., Longhi, S., & Xue, P. (2026) · Physical Review Letters · doi:10.1103/nqmq-8zsl
- Authors
- Musz, M., Kuś, M., & Życzkowski, K.
- Affiliations
- Center for Theoretical Physics (PL)
- Jagiellonian University (PL)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2013-02-13
- Volume
- 87
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2162782880
- Cited by
- 58
- References
- 67
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 3 · 2023: 3 · 2022: 4 · 2021: 4 · 2020: 2 · 2019: 10 · 2018: 7 · 2017: 1 · 2016: 1 · 2015: 4 · 2014: 4 · 2013: 2
- FWCI
- 4.06
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Homo Politicus (Academy of Humanities and Economics in Lodz) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- 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
- Haar measure, unitary groups, entanglement entropy, singular values, two-qubit gates, partial trace, maximally mixed state, nonlocality
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