Device-independent characterization of quantum instruments

Sebastian Wagner; Jean-Daniel Bancal; Nicolas Sangouard; Pavel Sekatski

doi:10.22331/q-2020-03-19-243

Device-independent characterization of quantum instruments

Sebastian Wagner, Jean-Daniel Bancal, Nicolas Sangouard, and Pavel Sekatski

Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Published:	2020-03-19, volume 4, page 243
Eprint:	arXiv:1812.02628v3
Doi:	https://doi.org/10.22331/q-2020-03-19-243
Citation:	Quantum 4, 243 (2020).

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Abstract

Among certification techniques, those based on the violation of Bell inequalities are appealing because they do not require assumptions on the underlying Hilbert space dimension and on the accuracy of calibration methods. Such device-independent techniques have been proposed to certify the quality of entangled states, unitary operations, projective measurements following von Neumann's model and rank-one positive-operator-valued measures (POVM). Here, we show that they can be extended to the characterization of quantum instruments with post-measurement states that are not fully determined by the Kraus operators but also depend on input states. We provide concrete certification recipes that are robust to noise.

► BibTeX data

@article{Wagner2020deviceindependent,
  doi = {10.22331/q-2020-03-19-243},
  url = {https://doi.org/10.22331/q-2020-03-19-243},
  title = {Device-independent characterization of quantum instruments},
  author = {Wagner, Sebastian and Bancal, Jean-Daniel and Sangouard, Nicolas and Sekatski, Pavel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {243},
  month = mar,
  year = {2020}
}

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[1] Xavier Valcarce, Julian Zivy, Nicolas Sangouard, and Pavel Sekatski, "Self-testing two-qubit maximally entangled states from generalized Clauser-Horne-Shimony-Holt tests", Physical Review Research 4 1, 013049 (2022).

[2] Nikolai Miklin, Jakub J. Borkała, and Marcin Pawłowski, "Semi-device-independent self-testing of unsharp measurements", Physical Review Research 2 3, 033014 (2020).

[3] Ivan Šupić and Joseph Bowles, "Self-testing of quantum systems: a review", Quantum 4, 337 (2020).

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[5] Jean-Daniel Bancal, Kai Redeker, Pavel Sekatski, Wenjamin Rosenfeld, and Nicolas Sangouard, "Self-testing with finite statistics enabling the certification of a quantum network link", Quantum 5, 401 (2021).

[6] Xinhui Li, Yukun Wang, Yunguang Han, and Shi-Ning Zhu, "Self-testing of different entanglement resources via fixed measurement settings", Physical Review A 106 5, 052418 (2022).

[7] Sumit Mukherjee and A. K. Pan, "Semi-device-independent certification of multiple unsharpness parameters through sequential measurements", Physical Review A 104 6, 062214 (2021).

[8] Kenneth Rudinger, Guilhem J. Ribeill, Luke C.G. Govia, Matthew Ware, Erik Nielsen, Kevin Young, Thomas A. Ohki, Robin Blume-Kohout, and Timothy Proctor, "Characterizing Midcircuit Measurements on a Superconducting Qubit Using Gate Set Tomography", Physical Review Applied 17 1, 014014 (2022).

[9] Pei-Sheng Lin, Tamás Vértesi, and Yeong-Cherng Liang, "Naturally restricted subsets of nonsignaling correlations: typicality and convergence", Quantum 6, 765 (2022).

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[11] Jędrzej Kaniewski, "Weak form of self-testing", Physical Review Research 2 3, 033420 (2020).

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[13] Roman Stricker, Davide Vodola, Alexander Erhard, Lukas Postler, Michael Meth, Martin Ringbauer, Philipp Schindler, Rainer Blatt, Markus Müller, and Thomas Monz, "Characterizing Quantum Instruments: From Nondemolition Measurements to Quantum Error Correction", PRX Quantum 3 3, 030318 (2022).

[14] Karthik Mohan, Armin Tavakoli, and Nicolas Brunner, "Sequential random access codes and self-testing of quantum measurement instruments", New Journal of Physics 21 8, 083034 (2019).

[15] Antoni Mikos-Nuszkiewicz and Jędrzej Kaniewski, "Extremal points of the quantum set in the CHSH scenario: conjectured analytical solution", arXiv:2302.10658, (2023).

[16] Tim Coopmans, Jedrzej Kaniewski, and Christian Schaffner, "Robust self-testing of two-qubit states", Physical Review A 99 5, 052123 (2019).

[17] Jędrzej Kaniewski, "A weak form of self-testing", arXiv:1910.00706, (2019).

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