Discrimination and certification of unknown quantum measurements

Aleksandra Krawiec1,2, Łukasz Pawela1, and Zbigniew Puchała1

1Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, 44-100 Gliwice, Poland
2AstroCeNT, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Rektorska 4, 00-614 Warsaw, Poland

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We study the discrimination of von Neumann measurements in the scenario when we are given a reference measurement and some other measurement. The aim of the discrimination is to determine whether the other measurement is the same as the first one. We consider the cases when the reference measurement is given without the classical description and when its classical description is known. Both cases are studied in the symmetric and asymmetric discrimination setups. Moreover, we provide optimal certification schemes enabling us to certify a known quantum measurement against the unknown one.

We are given two devices. The first device is a reference device. The second device can either be the same device as the first one or not. How can we verify if the second device is the same as the first one? We study this problem when the devices are quantum measurements. We present schemes for certification when the reference device is given with its description and when that description is not known.

► BibTeX data

► References

[1] Jens Eisert, Dominik Hangleiter, Nathan Walk, Ingo Roth, Damian Markham, Rhea Parekh, Ulysse Chabaud, and Elham Kashefi. ``Quantum certification and benchmarking''. Nature Reviews PhysicsPages 1–9 (2020).
https:/​/​doi.org/​10.1038/​s42254-020-0186-4

[2] Matteo Paris and Jaroslav Rehacek. ``Quantum state estimation''. Volume 649. Springer Science & Business Media. (2004).
https:/​/​doi.org/​10.1007/​b98673

[3] János A Bergou. ``Quantum state discrimination and selected applications''. Journal of Physics: Conference Series 84, 012001 (2007).
https:/​/​doi.org/​10.1364/​CQO.2007.CMF4

[4] Stephen M Barnett and Sarah Croke. ``Quantum state discrimination''. Advances in Optics and Photonics 1, 238–278 (2009).
https:/​/​doi.org/​10.1364/​AOP.1.000238

[5] Joonwoo Bae and Leong-Chuan Kwek. ``Quantum state discrimination and its applications''. Journal of Physics A: Mathematical and Theoretical 48, 083001 (2015).
https:/​/​doi.org/​10.1088/​1751-8113/​48/​8/​083001

[6] Antonio Acin. ``Statistical distinguishability between unitary operations''. Physical Review Letters 87, 177901 (2001).
https:/​/​doi.org/​10.1103/​PhysRevLett.87.177901

[7] Joonwoo Bae. ``Discrimination of two-qubit unitaries via local operations and classical communication''. Scientific Reports 5, 1–8 (2015).
https:/​/​doi.org/​10.1038/​srep18270

[8] Akinori Kawachi, Kenichi Kawano, François Le Gall, and Suguru Tamaki. ``Quantum query complexity of unitary operator discrimination''. IEICE TRANSACTIONS on Information and Systems 102, 483–491 (2019).
https:/​/​doi.org/​10.1587/​transinf.2018FCP0012

[9] Massimiliano F Sacchi. ``Optimal discrimination of quantum operations''. Physical Review A 71, 062340 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.71.062340

[10] Massimiliano F Sacchi. ``Entanglement can enhance the distinguishability of entanglement-breaking channels''. Physical Review A 72, 014305 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.72.014305

[11] Marco Piani and John Watrous. ``All entangled states are useful for channel discrimination''. Physical Review Letters 102, 250501 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.102.250501

[12] Runyao Duan, Yuan Feng, and Mingsheng Ying. ``Perfect distinguishability of quantum operations''. Physical Review Letters 103, 210501 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.210501

[13] Guoming Wang and Mingsheng Ying. ``Unambiguous discrimination among quantum operations''. Physical Review A 73, 042301 (2006).
https:/​/​doi.org/​10.1103/​PhysRevA.73.042301

[14] Aleksandra Krawiec, Łukasz Pawela, and Zbigniew Puchała. ``Excluding false negative error in certification of quantum channels''. Scientific Reports 11, 1–11 (2021).
https:/​/​doi.org/​10.1038/​s41598-021-00444-x

[15] Mário Ziman. ``Process positive-operator-valued measure: A mathematical framework for the description of process tomography experiments''. Physical Review A 77, 062112 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.77.062112

[16] Michal Sedlák and Mário Ziman. ``Unambiguous comparison of unitary channels''. Physical Review A 79, 012303 (2009).
https:/​/​doi.org/​10.1103/​PhysRevA.79.012303

[17] Mário Ziman and Michal Sedlák. ``Single-shot discrimination of quantum unitary processes''. Journal of Modern Optics 57, 253–259 (2010).
https:/​/​doi.org/​10.1080/​09500340903349963

[18] Yujun Choi, Tanmay Singal, Young-Wook Cho, Sang-Wook Han, Kyunghwan Oh, Sung Moon, Yong-Su Kim, and Joonwoo Bae. ``Single-copy certification of two-qubit gates without entanglement''. Physical Review Applied 18, 044046 (2022).
https:/​/​doi.org/​10.1103/​PhysRevApplied.18.044046

[19] Mark Hillery, Erika Andersson, Stephen M Barnett, and Daniel Oi. ``Decision problems with quantum black boxes''. Journal of Modern Optics 57, 244–252 (2010).
https:/​/​doi.org/​10.1080/​09500340903203129

[20] Akihito Soeda, Atsushi Shimbo, and Mio Murao. ``Optimal quantum discrimination of single-qubit unitary gates between two candidates''. Physical Review A 104, 022422 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.104.022422

[21] Yutaka Hashimoto, Akihito Soeda, and Mio Murao. ``Comparison of unknown unitary channels with multiple uses'' (2022). arXiv:2208.12519.
arXiv:2208.12519

[22] John Watrous. ``The theory of quantum information''. Cambridge University Press. (2018).
https:/​/​doi.org/​10.1017/​9781316848142

[23] Zbigniew Puchała, Łukasz Pawela, Aleksandra Krawiec, and Ryszard Kukulski. ``Strategies for optimal single-shot discrimination of quantum measurements''. Physical Review A 98, 042103 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.042103

[24] Zbigniew Puchała, Łukasz Pawela, Aleksandra Krawiec, Ryszard Kukulski, and Michał Oszmaniec. ``Multiple-shot and unambiguous discrimination of von Neumann measurements''. Quantum 5, 425 (2021).
https:/​/​doi.org/​10.22331/​q-2021-04-06-425

[25] Paulina Lewandowska, Aleksandra Krawiec, Ryszard Kukulski, Łukasz Pawela, and Zbigniew Puchała. ``On the optimal certification of von Neumann measurements''. Scientific Reports 11, 1–16 (2021).
https:/​/​doi.org/​10.1038/​s41598-022-10219-7

[26] M Miková, M Sedlák, I Straka, M Mičuda, M Ziman, M Ježek, M Dušek, and J Fiurášek. ``Optimal entanglement-assisted discrimination of quantum measurements''. Physical Review A 90, 022317 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.90.022317

[27] Mario Ziman, Teiko Heinosaari, and Michal Sedlák. ``Unambiguous comparison of quantum measurements''. Physical Review A 80, 052102 (2009).
https:/​/​doi.org/​10.1103/​PhysRevA.80.052102

[28] Michal Sedlák and Mário Ziman. ``Optimal single-shot strategies for discrimination of quantum measurements''. Physical Review A 90, 052312 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.90.052312

[29] Paulina Lewandowska, Łukasz Pawela, and Zbigniew Puchała. ``Strategies for single-shot discrimination of process matrices''. Scientific Reports 13, 3046 (2023).
https:/​/​doi.org/​10.1038/​s41598-023-30191-0

[30] Kieran Flatt, Hanwool Lee, Carles Roch I Carceller, Jonatan Bohr Brask, and Joonwoo Bae. ``Contextual advantages and certification for maximum-confidence discrimination''. PRX Quantum 3, 030337 (2022).
https:/​/​doi.org/​10.1103/​PRXQuantum.3.030337

[31] Ion Nechita, Zbigniew Puchała, Łukasz Pawela, and Karol Życzkowski. ``Almost all quantum channels are equidistant''. Journal of Mathematical Physics 59, 052201 (2018).
https:/​/​doi.org/​10.1063/​1.5019322

[32] Carl W Helstrom. ``Quantum detection and estimation theory''. Journal of Statistical Physics 1, 231–252 (1969).
https:/​/​doi.org/​10.1007/​BF01007479

[33] Farzin Salek, Masahito Hayashi, and Andreas Winter. ``Usefulness of adaptive strategies in asymptotic quantum channel discrimination''. Physical Review A 105, 022419 (2022).
https:/​/​doi.org/​10.1103/​PhysRevA.105.022419

[34] Mark M Wilde, Mario Berta, Christoph Hirche, and Eneet Kaur. ``Amortized channel divergence for asymptotic quantum channel discrimination''. Letters in Mathematical Physics 110, 2277–2336 (2020).
https:/​/​doi.org/​10.1007/​s11005-020-01297-7

[35] Sisi Zhou and Liang Jiang. ``Asymptotic theory of quantum channel estimation''. PRX Quantum 2, 010343 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010343

[36] Tom Cooney, Milán Mosonyi, and Mark M Wilde. ``Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication''. Communications in Mathematical Physics 344, 797–829 (2016).
https:/​/​doi.org/​10.1007/​s00220-016-2645-4

[37] Z Puchała and JA Miszczak. ``Symbolic integration with respect to the Haar measure on the unitary groups''. Bulletin of the Polish Academy of Sciences. Technical Sciences 65 (2017).
https:/​/​doi.org/​10.1515/​bpasts-2017-0003

[38] Benoı̂t Collins and Piotr Śniady. ``Integration with respect to the Haar measure on unitary, orthogonal and symplectic group''. Communications in Mathematical Physics 264, 773–795 (2006).
https:/​/​doi.org/​10.1007/​s00220-006-1554-3

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2024-04-12 06:17:04). On SAO/NASA ADS no data on citing works was found (last attempt 2024-04-12 06:17:04).