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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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.

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[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] Nikolai Miklin, Jakub J. Borkała, and Marcin Pawłowski, "Semi-device-independent self-testing of unsharp measurements", arXiv:1903.12533, Physical Review Research 2 3, 033014 (2020).

[2] Ivan Šupić and Joseph Bowles, "Self-testing of quantum systems: a review", arXiv:1904.10042.

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

[4] 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", arXiv:1812.09117.

[5] 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).

[6] Jędrzej Kaniewski, "A weak form of self-testing", arXiv:1910.00706.

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

[8] Flavio Baccari, Remigiusz Augusiak, Ivan Šupić, and Antonio Acín, "Device-independent certification of entangled subspaces", arXiv:2003.02285.

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