For minimum-error channel discrimination tasks that involve only unitary channels, we show that sequential strategies may outperform the parallel ones. Additionally, we show that general strategies that involve indefinite causal order are also advantageous for this task. However, for the task of discriminating a uniformly distributed set of unitary channels that forms a group, we show that parallel strategies are, indeed, optimal, even when compared to general strategies. We also show that strategies based on the quantum switch cannot outperform sequential strategies in the discrimination of unitary channels. Finally, we derive an absolute upper bound for the maximal probability of successfully discriminating any set of unitary channels with any number of copies for the most general strategies that are suitable for channel discrimination. Our bound is tight since it is saturated by sets of unitary channels forming a group k-design.
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April 2022
Research Article|
April 18 2022
Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
Jessica Bavaresco
;
Jessica Bavaresco
a)
1
Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences
, Boltzmanngasse 3, A-1090 Vienna, Austria
a)Author to whom correspondence should be addressed: jessica.bavaresco@oeaw.ac.at
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Mio Murao
;
Mio Murao
2
Department of Physics, Graduate School of Science, The University of Tokyo
, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
3
Trans-scale Quantum Science Institute, The University of Tokyo
, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
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Marco Túlio Quintino
Marco Túlio Quintino
1
Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences
, Boltzmanngasse 3, A-1090 Vienna, Austria
4
Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna
, Boltzmanngasse 5, A-1090 Vienna, Austria
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a)Author to whom correspondence should be addressed: jessica.bavaresco@oeaw.ac.at
J. Math. Phys. 63, 042203 (2022)
Article history
Received:
October 19 2021
Accepted:
March 13 2022
Citation
Jessica Bavaresco, Mio Murao, Marco Túlio Quintino; Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies. J. Math. Phys. 1 April 2022; 63 (4): 042203. https://doi.org/10.1063/5.0075919
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