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

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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.

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Cited by

[1] 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).

[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", arXiv:1904.10042, Quantum 4, 337 (2020).

[4] Geng Chen, Wen-Hao Zhang, Peng Yin, Chuan-Feng Li, and Guang-Can Guo, "Device-independent characterization of entanglement based on bell nonlocality", Fundamental Research 1 1, 27 (2021).

[5] Jędrzej Kaniewski, "Weak form of self-testing", arXiv:1910.00706, Physical Review Research 2 3, 033420 (2020).

[6] Flavio Baccari, Remigiusz Augusiak, Ivan Šupić, and Antonio Acín, "Device-Independent Certification of Genuinely Entangled Subspaces", Physical Review Letters 125 26, 260507 (2020).

[7] 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).

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

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