Gauge invariant information concerning quantum channels

Łukasz Rudnicki; Zbigniew Puchała; Karol Zyczkowski

doi:10.22331/q-2018-04-11-60

Gauge invariant information concerning quantum channels

Łukasz Rudnicki^1,2, Zbigniew Puchała^3,4, and Karol Zyczkowski^2,4

¹Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, D-50937, Cologne, Germany
²Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
³Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ulica Bałtycka 5, 44-100 Gliwice, Poland
⁴Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland

Published:	2018-04-11, volume 2, page 60
Eprint:	arXiv:1707.06926v2
Doi:	https://doi.org/10.22331/q-2018-04-11-60
Citation:	Quantum 2, 60 (2018).

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Abstract

Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the complex spectrum of the superoperator to provide necessary conditions relevant for complete positivity of qubit channels and to express various metrics such as average gate fidelity.

Featured image: Exemplary ranges of eigenvalues for qubit quantum channels. Within the Gate Set Tomography, due to its gauge symmetry, the only meaningful characterization of a channel is provided by
the eigenvalues.

► BibTeX data

@article{Rudnicki2018gaugeinvariant,
  doi = {10.22331/q-2018-04-11-60},
  url = {https://doi.org/10.22331/q-2018-04-11-60},
  title = {Gauge invariant information concerning quantum channels},
  author = {Rudnicki, {\L{}}ukasz and Pucha{\l{}}a, Zbigniew and Zyczkowski, Karol},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {60},
  month = apr,
  year = {2018}
}

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[8] Marco Cattaneo, Matteo A.C. Rossi, Guillermo García-Pérez, Roberta Zambrini, and Sabrina Maniscalco, "Quantum Simulation of Dissipative Collective Effects on Noisy Quantum Computers", PRX Quantum 4 1, 010324 (2023).

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