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).

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

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}
}

► References

[1] B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, R. Hanson, Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature 526, 682 (2015).
https://doi.org/10.1038/nature15759

[2] L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne, M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J. Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, S. W. Nam, Strong Loophole-Free Test of Local Realism, Phys. Rev. Lett. 115, 250402 (2015).
https://doi.org/10.1103/PhysRevLett.115.250402

[3] M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J-Å. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, A. Zeilinger, Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons, Phys. Rev. Lett. 115, 250401 (2015).
https://doi.org/10.1103/PhysRevLett.115.250401

[4] W. Rosenfeld, D. Burchardt, R. Garthoff, K. Redeker, N. Ortegel, M. Rau, H. Weinfurter, Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes, Phys. Rev. Lett. 119, 010402 (2017).
https://doi.org/10.1103/PhysRevLett.119.010402

[5] J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1, 195 (1964).
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195

[6] R. Colbeck, Quantum And Relativistic Protocols For Secure Multi-Party Computation, Ph.D. thesis, (2009).
arXiv:0911.3814

[7] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, C. Monroe, Random numbers certified by Bell’s theorem, Nature 464, 1021 (2010).
https://doi.org/10.1038/nature09008

[8] B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, Detection-Loophole-Free Test of Quantum Nonlocality, and Applications, Phys. Rev. Lett. 111, 130406 (2013).
https://doi.org/10.1103/PhysRevLett.111.130406

[9] Y. Liu, X. Yuan, M-H. Li, W. Zhang, Q. Zhao, J. Zhong, Y. Cao, Y-H. Li, L-K. Chen, H. Li, T. Peng, Y-A. Chen, C-Z. Peng, S-C. Shi, Z. Wang, L. You, X. Ma, J. Fan, Q. Zhang, J-W. Pan, High-Speed Device-Independent Quantum Random Number Generation without a Detection Loophole, Phys. Rev. Lett. 120, 010503 (2018).
https://doi.org/10.1103/PhysRevLett.120.010503

[10] Y. Liu, Q. Zhao, M-H. Li, J-Y. Guan, Y. Zhang, B. Bai, W. Zhang, W-Z. Liu, C. Wu, X. Yuan, H. Li, W. J. Munro, Z. Wang, L. You, J. Zhang, X. Ma, J. Fan, Q. Zhang, J-W. Pan, Device-independent quantum random-number generation, Nature 562, 548 (2018).
https://doi.org/10.1038/s41586-018-0559-3

[11] P. Bierhorst, E. Knill, S. Glancy, Y. Zhang, A. Mink, S. Jordan, A. Rommal, Y-K. Liu, B. Christensen, S. W. Nam, M. J. Stevens, L. K. Shalm, Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals, Nature 556, 223 (2018).
https://doi.org/10.1038/s41586-018-0019-0

[12] L. Shen, J. Lee, L. P. Thinh, J-D. Bancal, A. Cerè, A. Lamas-Linares, A. Lita, T. Gerrits, S. W. Nam, V. Scarani, C. Kurtsiefer Randomness Extraction from Bell Violation with Continuous Parametric Down-Conversion, Phys. Rev. Lett. 121, 150402 (2018).
https://doi.org/10.1103/PhysRevLett.121.150402

[13] J. F. Clauser, M. A. Horne, A. Shimony, R.A. Holt, Proposed Experiment to Test Local Hidden-Variable Theories, Phys. Rev. Lett. 23, 880 (1969).
https://doi.org/10.1103/PhysRevLett.23.880

[14] S. Popescu, D. Rohrlich, Which states violate Bell's inequality maximally?, Phys. Lett. A 169, 411 (1992).
https://doi.org/10.1016/0375-9601(92)90819-8

[15] M. McKague, T. H. Yang, V. Scarani, Robust self-testing of the singlet, J. Phys. A: Math. Theor. 45, 455304 (2012).
https://doi.org/10.1088/1751-8113/45/45/455304

[16] D. Mayers, A. Yao, Quantum Cryptography with Imperfect Apparatus, Proceedings of the 39th IEEE Conference on Foundations of Computer Science, 1998, page 503, see also Self testing quantum apparatus, Quant. Inf. Comput. 4, 273 (2004).
https://doi.org/10.26421/QIC4.4
arXiv:quant-ph/9809039

[17] M. McKague, Interactive Proofs for BQP via Self-Tested Graph States, Theory of Computing, 12, 3 (2016).
https://doi.org/10.4086/toc.2016.v012a003

[18] A. Coladangelo, K.T. Goh, V. Scarani, All Pure Bipartite Entangled States can be Self-Tested, Nat. Comm. 8, 15485 (2017).
https://doi.org/10.1038/ncomms15485

[19] X. Wu, Y. Cai, T. H. Yang, H. Nguyen Le, J-D. Bancal, V. Scarani, Robust self-testing of the three-qubit W state, Phys. Rev. A 90, 042339 (2014).
https://doi.org/10.1103/PhysRevA.90.042339

[20] J-D. Bancal, M. Navascués, V. Scarani, T. Vértesi, T. H. Yang, Physical characterization of quantum devices from nonlocal correlations, Phys. Rev. A 91, 022115 (2015).
https://doi.org/10.1103/PhysRevA.91.022115

[21] S-L. Chen, C. Budroni, Y-C. Liang, Y-N. Chen, Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing, Phys. Rev. Lett. 116, 240401 (2016).
https://doi.org/10.1103/PhysRevLett.116.240401

[22] D. Cavalcanti, P. Skrzypczyk, Quantitative relations between measurement incompatibility, quantum steering, and nonlocality, Phys. Rev. A 93, 052112 (2016).
https://doi.org/10.1103/PhysRevA.93.052112

[23] J. Kaniewski, Self-testing of binary observables based on commutation, Phys. Rev. A 95, 062323 (2017).
https://doi.org/10.1103/PhysRevA.95.062323

[24] J. Bowles, I. Šupić, D. Cavalcanti, A. Acín, Self-testing of Pauli observables for device-independent entanglement certification, Phys. Rev. A 98, 042336 (2018).
https://doi.org/10.1103/PhysRevA.98.062336

[25] M-O. Renou, J. Kaniewski, N. Brunner, Self-Testing Entangled Measurements in Quantum Networks, Phys. Rev. Lett. 121, 250507 (2018).
https://doi.org/10.1103/PhysRevLett.121.250507

[26] J-D. Bancal, N. Sangouard, P. Sekatski, Noise-Resistant Device-Independent Certification of Bell State Measurements, Phys. Rev. Lett. 121, 250506 (2018).
https://doi.org/10.1103/PhysRevLett.121.250506

[27] P. Sekatski, J-D. Bancal, S. Wagner, N. Sangouard, Certifying the Building Blocks of Quantum Computers from Bell’s Theorem, Phys. Rev. Lett. 121, 180505 (2018).
https://doi.org/10.1103/PhysRevLett.121.180505

[28] E. S. Gómez, S. Gómez, P. González, G. Cañas, J. F. Barra, A. Delgado, G. B. Xavier, A. Cabello, M. Kleinmann, T. Vértesi, G. Lima, Device-Independent Certification of a Nonprojective Qubit Measurement, Phys. Rev. Lett. 117, 260401 (2016).
https://doi.org/10.1103/PhysRevLett.117.260401

[29] M. Smania, P. Mironowicz, M. Nawareg, M. Pawłowski, A. Cabello, M. Bourennane, Experimental certification of an informationally complete quantum measurement in a device-independent protocol, Optica 7,123-128 (2020).
https://doi.org/10.1364/OPTICA.377959

[30] E. B. Davies, J. T. Lewis, An operational approach to quantum probability, Comm. Math. Phys. 17, 239 (1970).
https://doi.org/10.1007/BF01647093

[31] J. A. Gross, C. M. Caves, G. J. Milburn, J. Combes, Qubit models of weak continuous measurements: markovian conditional and open-system dynamics, Quantum Sci. Technol. 3, 024005 (2018).
https://doi.org/10.1088/2058-9565/aaa39f

[32] R. Silva, N. Gisin, Y. Guryanova, S. Popescu, Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements, Phys. Rev. Lett. 114, 250401 (2015).
https://doi.org/10.1103/PhysRevLett.114.250401

[33] F. J. Curchod, M. Johansson, R. Augusiak, M. J. Hoban, P. Wittek, A. Acín Unbounded randomness certification using sequences of measurements, Phys. Rev. A 95, 020102 (2017).
https://doi.org/10.1103/PhysRevA.95.020102

[34] F. J. Curchod, M. Johansson, R. Augusiak, M. J. Hoban, P. Wittek, A. Acín, A Single Entangled System Is an Unbounded Source of Nonlocal Correlations and of Certified Random Numbers, 12$^\text{th}$ Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017), Leibniz International Proceedings in Informatics (LIPIcs) 73, 1:1 (2018).
https://doi.org/10.4230/LIPIcs.TQC.2017.1

[35] B. Coyle, M.J. Hoban, E. Kashefi, One-Sided Device-Independent Certification of Unbounded Random Numbers, EPTCS 273, 14 (2018).
https://doi.org/10.4204/EPTCS.273.2

[36] K. Banaszek, I. Devetak, Fidelity trade-off for finite ensembles of identically prepared qubits, Phys. Rev. A 64, 052307 (2001).
https://doi.org/10.1103/PhysRevA.64.052307

[37] M-D. Choi, Completely positive linear maps on complex matrices, Linear Algebra Appl., 10, 285 (1975).
https://doi.org/10.1016/0024-3795(75)90075-0

[38] A. Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep. Math. Phys. 3, 275 (1972).
https://doi.org/10.1016/0034-4877(72)90011-0

[39] M. Raginsky, A fidelity measure for quantum channels, Phys. Lett. A 290, 11 (2001).
https://doi.org/10.1016/S0375-9601(01)00640-5

[40] V. P. Belavkin, G. M. D’Ariano, M. Raginsky, Operational distance and fidelity for quantum channels, J. Math. Phys. 46, 062106 (2005).
https://doi.org/10.1063/1.1904510

[41] J. Kaniewski, Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities, Phys. Rev. Lett. 117, 070402 (2016).
https://doi.org/10.1103/PhysRevLett.117.070402

[42] P. Sekatski et al., in preparation.

[43] A. Acín, S. Massar, S. Pironio, Randomness versus Nonlocality and Entanglement, Phys. Rev. Lett, 108, 100402 (2012).
https://doi.org/10.1103/PhysRevLett.108.100402

[44] C. Bamps, S. Pironio, Sum-of-squares decompositions for a family of Clauser-Horne-Shimony-Holt-like inequalities and their application to self-testing, Phys. Rev. A 91, 052111 (2015).
https://doi.org/10.1103/PhysRevA.91.052111

[45] T. Coopmans, J. Kaniewski, C. Schaffner, Robust self-testing of two-qubit states, Phys. Rev. A 99, 052123 (2019).
https://doi.org/10.1103/PhysRevA.99.052123

Cited by

[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] Kai-Siang Chen, Gelo Noel M. Tabia, Jebarathinam Chellasamy, Shiladitya Mal, Jun-Yi Wu, and Yeong-Cherng Liang, "Quantum correlations on the no-signaling boundary: self-testing and more", Quantum 7, 1054 (2023).

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

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

[5] N. Gigena and J. Kaniewski, "Quantum value for a family of I3322 -like Bell functionals", Physical Review A 106 1, 012401 (2022).

[6] Antoni Mikos-Nuszkiewicz and Jędrzej Kaniewski, "Extremal points of the quantum set in the Clauser-Horne-Shimony-Holt scenario: Conjectured analytical solution", Physical Review A 108 1, 012212 (2023).

[7] Pavel Sekatski, Jean-Daniel Bancal, Marie Ioannou, Mikael Afzelius, and Nicolas Brunner, "Toward the Device-Independent Certification of a Quantum Memory", Physical Review Letters 131 17, 170802 (2023).

[8] 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).

[9] 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).

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

[11] 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).

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

[13] 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).

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

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

[16] 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).

[17] 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).

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

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

[20] Satoshi Ishizaka, "Geometrical self-testing of partially entangled two-qubit states", New Journal of Physics 22 2, 023022 (2020).

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

The above citations are from Crossref's cited-by service (last updated successfully 2023-11-29 19:37:33) and SAO/NASA ADS (last updated successfully 2023-11-29 19:37:34). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.