Robust certification of arbitrary outcome quantum measurements from temporal correlations

Debarshi Das1,2, Ananda G. Maity1, Debashis Saha1, and A. S. Majumdar1

1S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
2Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, UK

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Certification of quantum devices received from unknown providers is a primary requirement before utilizing the devices for any information processing task. Here, we establish a protocol for certification of a particular set of $d$-outcome quantum measurements (with $d$ being arbitrary) in a setup comprising of a preparation followed by two measurements in sequence. We propose a set of temporal inequalities pertaining to different $d$ involving correlation functions corresponding to successive measurement outcomes, that are not satisfied by quantum devices. Using quantum violations of these inequalities, we certify specific $d$-outcome quantum measurements under some minimal assumptions which can be met in an experiment efficiently. Our certification protocol neither requires entanglement, nor any prior knowledge about the dimension of the system under consideration. We further show that our protocol is robust against practical non-ideal realizations. Finally, as an offshoot of our protocol, we present a scheme for secure certification of genuine quantum randomness.

With emerging quantum technology, it is important to design experiments which can test whether the quantum devices received from unknown providers function properly. Certification protocols are designed for this purpose. Since quantum measurements are one of the key resources of modern quantum technologies and play a crucial role in revealing unique quantum phenomena, we aim to design certification protocols of quantum measurements having arbitrary number of outcomes with the desiderata of efficiency and less resource consumption. In particular, we propose a method to certify a particular set of quantum measurements having fundamental significance as well as information theoretic applications using temporal quantum correlations. Our proposed method works under some minimal assumptions which can be met in an experiment efficiently. However, our method requires neither entanglement between space-like separated systems, nor any prior knowledge about the dimension of the system under consideration. We also demonstrate the efficacy of our protocol in practical non-ideal situations. Although we propose certification protocol of some specific quantum measurements with arbitrary number of outcomes, the method presented by us is quite general and can be immediately applied in different contexts to certify a wide range of quantum measurements employing temporal quantum correlations. Finally, we present genuine quantum randomness certification as an application of our proposed protocol.

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[1] I. L. Chuang and M. A. Nielsen, Prescription for experimental determination of the dynamics of a quantum black box, J. Mod. Opt. 44, 2455 (1997).

[2] J. F. Poyatos, J. I. Cirac, and P. Zoller, Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate, Phys. Rev. Lett. 78, 390 (1997).

[3] Z. Hradil, Quantum-state estimation, Phys. Rev. A, 55, R1561(R) (1997).

[4] J. Helsen, J. J. Wallman, S. T. Flammia, and S. Wehner, Multiqubit randomized benchmarking using few samples, Phys. Rev. A, 100, 032304 (2019).

[5] E. Magesan, J. M. Gambetta, and J. Emerson, Scalable and Robust Randomized Benchmarking of Quantum Processes, Phys. Rev. Lett., 106, 180504 (2011).

[6] E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Randomized benchmarking of quantum gates, Phys. Rev. A, 77, 012307 (2008).

[7] J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Quantum certification and benchmarking, Nat Rev Phys 2, 382 (2020).

[8] D. Mayers, and A. Yao, Quantum cryptography with imperfect apparatus, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280), 1998, pp. 503-509.

[9] D. Mayers, and A. Yao, Self testing quantum apparatus, Quantum Inf. Comput. 4, 273 (2004).

[10] I. Supic, and J. Bowles, Self-testing of quantum systems: a review, Quantum 4, 337 (2020).

[11] A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Device-Independent Security of Quantum Cryptography against Collective Attacks, Phys. Rev. Lett., 98, 230501 (2007).

[12] S. Pironio, A. Acín, S. Massar, A. B. Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning and C. Monroe, Random numbers certified by Bell’s theorem, Nature, 464, 1021 (2010).

[13] B. W. Reichardt, F. Unger, and U. Vazirani, Classical command of quantum systems, Nature 496, 456 (2013).

[14] M. McKague, T. H. Yang, and V. Scarani, Robust self-testing of the singlet, J. Phys. A: Math. Theor. 45, 455304 (2012).

[15] T. H. Yang and M. Navascues, Robust self-testing of unknown quantum systems into any entangled two-qubit states, Phys. Rev. A 87, 050102(R) (2013).

[16] C. Bamps and 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).

[17] A. Coladangelo, K. T. Goh, and V. Scarani, All pure bipartite entangled states can be self-tested, Nat Commun 8, 15485 (2017).

[18] Y. Wang, X. Wu, and V. Scarani, All the self-testings of the singlet for two binary measurements, New J. Phys. 18, 025021 (2016).

[19] I. Supic, R. Augusiak, A Salavrakos, and A. Acín, Self-testing protocols based on the chained Bell inequalities, New J. Phys. 18, 035013 (2016).

[20] I. Supic, A. Coladangelo, R. Augusiak, and A. Acín, Self-testing multipartite entangled states through projections onto two systems, New J. Phys. 20, 083041 (2018).

[21] I. Supic and M. J. Hoban, Self-testing through EPR-steering, New J. Phys. 18, 075006 (2016).

[22] S. Goswami, B. Bhattacharya, D. Das, S. Sasmal, C. Jebaratnam, and A. S. Majumdar, One-sided device-independent self-testing of any pure two-qubit entangled state, Phys. Rev. A 98, 022311 (2018).

[23] Z. Bian, A. S. Majumdar, C. Jebaratnam, K. Wang, L. Xiao, X. Zhan, Y. Zhang, and P. Xue, Experimental demonstration of one-sided device-independent self-testing for any pure two-qubit entangled state, Phys. Rev. A 101, 020301(R) (2020).

[24] H. Shrotriya, K. Bharti, and L.-C. Kwek, Robust semi-device-independent certification of all pure bipartite maximally entangled states via quantum steering, Phys. Rev. Research 3, 033093 (2021).

[25] S. Sarkar, D. Saha, and R. Augusiak, Certification of incompatible measurements using quantum steering, arXiv:2107.02937.

[26] S. Sarkar, J. J. Borkała, C. Jebarathinam, O. Makuta, D. Saha, and R. Augusiak Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario, arXiv:2110.15176.

[27] A. Tavakoli, J. Kaniewski, T. Vertesi, D. Rosset, and N. Brunner, Self-testing quantum states and measurements in the prepare-and-measure scenario, Phys. Rev. A 98, 062307 (2018).

[28] K. Bharti, M. Ray, A. Varvitsiotis, N. A. Warsi, A. Cabello, and L.-C. Kwek, Robust Self-Testing of Quantum Systems via Noncontextuality Inequalities, Phys. Rev. Lett. 122, 250403 (2019).

[29] D. Saha, R. Santos, and R. Augusiak, Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices, Quantum 4, 302 (2020).

[30] J. D. Bancal, N. Sangouard, and P. Sekatski, Noise-Resistant Device-Independent Certification of Bell State Measurements, Phys. Rev. Lett. 121, 250506 (2018).

[31] M. O. Renou, J. Kaniewski, and N. Brunner, Self-Testing Entangled Measurements in Quantum Networks, Phys. Rev. Lett. 121, 250507 (2018).

[32] J. Kaniewski, Self-testing of binary observables based on commutation, Phys. Rev. A 95, 062323 (2017).

[33] M. McKague and M. Mosca, Generalized Self-testing and the Security of the 6-State Protocol, Theory of Quantum Computation, Communication, and Cryptography, edited by W. van Dam, V. M. Kendon, and S. Severini (Springer-Verlag Berlin Heidelberg, 2011) pp. 113–130.

[34] J. Bowles, I. Supic, D. Cavalcanti, and A. Acín, Self-testing of Pauli observables for device-independent entanglement certification, Phys. Rev. A, 98 042336 (2018).

[35] A. G. Maity, S. Mal, C. Jebarathinam, and A. S. Majumdar, Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction, Phys. Rev. A, 103, 062604 (2021).

[36] A. Salavrakos, R. Augusiak, J. Tura, P. Wittek, A. Acín, and S. Pironio, Bell Inequalities Tailored to Maximally Entangled States, Phys. Rev. Lett. 119, 040402 (2017).

[37] S. Sarkar, D. Saha, J. Kaniewski, and R. Augusiak, Self-testing quantum systems of arbitrary local dimension with minimal number of measurements, npj Quantum Inf 7, 151 (2021).

[38] P. Imany, J. A. Jaramillo-Villegas, M. S. Alshaykh, J. M. Lukens, O. D. Odele, A. J. Moore, D. E. Leaird, M. Qi, and A. M. Weiner, High-dimensional optical quantum logic in large operational spaces, npj Quantum Inf 5, 59 (2019).

[39] S. Wang, Z.-Q. Yin, H. F. Chau, W. Chen, C. Wang, G.-C. Guo, and Z.-F. Han, Proof-of-principle experimental realization of a qubit-like qudit-based quantum key distribution scheme, Quantum Sci. Technol. 3, 025006 (2018).

[40] Y.-C. Jeong, J.-C. Lee, and Y.-H. Kim, Experimental implementation of a fully controllable depolarizing quantum operation, Phys. Rev. A 87, 014301 (2013).

[41] M. Frey, D. Collins, and K. Gerlach, Probing the qudit depolarizing channel, J. Phys. A: Math. Theor. 44, 205306 (2011).

[42] M. Ahmed, and L. Young, Integrated optic series and multibranch interferometers, Journal of Lightwave Technology, 3, 77-82 (1985).

[43] A. Melloni, G. Cusmai, R. Costa, F. Morichetti, and M. Martinelli, Three-arm Mach-Zehnder interferometers, Integrated Photonics Research and Applications/​Nanophotonics, Technical Digest (CD) (Optica Publishing Group, 2006), paper IMC1.

[44] Y.-C. Liang, C.-W. Lim, and D.-L. Deng, Reexamination of a multisetting Bell inequality for qudits, Phys. Rev. A 80, 052116 (2009).

[45] J.-D. Bancal, C. Branciard, N. Brunner, N. Gisin, and Y.-C. Liang, A framework for the study of symmetric full-correlation Bell-like inequalities, J. Phys. A: Math. Theor. 45, 125301 (2012).

[46] A. J. Leggett, and A. Garg, Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54, 857 (1985).

[47] C. Brukner, S. Taylor, S. Cheung, and V. Vedral, Quantum Entanglement in Time, arXiv: quant-ph/​0402127.

[48] D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, Bell Inequalities for Arbitrarily High-Dimensional Systems, Phys. Rev. Lett. 88, 040404 (2002).

[49] J. Barrett, A. Kent, and S. Pironio, Maximally Nonlocal and Monogamous Quantum Correlations, Phys. Rev. Lett. 97, 170409 (2006).

[50] N. Brunner, S. Pironio, A. Acín, N. Gisin, A. A. Méthot, and V. Scarani, Testing the Dimension of Hilbert Spaces, Phys. Rev. Lett. 100, 210503 (2008).

[51] Y. Cai, J.-D. Bancal, J. Romero and V. Scarani, A new device-independent dimension witness and its experimental implementation, J. Phys. A: Math. Theor. 49, 305301 (2016).

[52] W. Cong, Y. Cai, J.-D. Bancal and V. Scarani, Witnessing Irreducible Dimension, Phys. Rev. Lett. 119, 080401 (2017).

[53] C. Brukner, M. Zukowski, and A. Zeilinger, Quantum Communication Complexity Protocol with Two Entangled Qutrits, Phys. Rev. Lett. 89, 197901 (2002).

[54] D. Martínez, A. Tavakoli, M. Casanova, G. Canas, B. Marques, and G. Lima, High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell's Theorem, Phys. Rev. Lett. 121, 150504 (2018).

[55] A. Hameedi, A. Tavakoli, B. Marques, and M. Bourennane, Communication Games Reveal Preparation Contextuality, Phys. Rev. Lett. 119, 220402 (2017).

[56] H. Mikami and T. Kobayashi, Remote preparation of qutrit states with biphotons, Phys. Rev. A, 75, 022325 (2007).

[57] L. Masanes, S. Pironio, and A. Acín, Secure device-independent quantum key distribution with causally independent measurement devices, Nat. Comm., 2, 238 (2011).

[58] T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, Security of quantum key distributions with entangled qudits, Phys. Rev. A 69, 032313 (2004).

[59] P. Skrzypczyk, and D. Cavalcanti, Maximal Randomness Generation from Steering Inequality Violations Using Qudits, Phys. Rev. Lett., 120, 260401 (2018).

[60] M. Zukowski, A. Zeilinger, and M. A. Horne, Realizable higher-dimensional two-particle entanglements via multiport beam splitters, Phys. Rev. A 55, 2564 (1997).

[61] A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett and E. Andersson, Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities, Nat. Phys. 7, 677 (2011).

[62] P. Busch, Unsharp reality and joint measurements for spin observables, Phys. Rev. D 33, 2253 (1986).

[63] P. Busch, and J. Singh, Lüders theorem for unsharp quantum measurements, Phys. Lett. A 249, 10 (1998).

[64] M. B. Plenio, and P. L. Knight, The quantum-jump approach to dissipative dynamics in quantum optics, Rev. Mod. Phys. 70, 101 (1998).

[65] J. Kaniewski, I. Supic, J. Tura, F. Baccari, A. Salavrakos, and R. Augusiak, Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems Quantum 3, 198 (2019).

[66] C. E. Shannon, Communication theory of secrecy systems, The Bell System Technical Journal, 28, 4 (1949).

[67] I. Gianani, Y. S. Teo, V. Cimini, H. Jeong, G. Leuchs, M. Barbieri, and L. L. Sánchez-Soto, PRX Quantum 1, 020307 (2020).

[68] S. Sarkar, and R. Augusiak, Self-testing of multipartite GHZ states of arbitrary local dimension with arbitrary number of measurements per party, Phys. Rev. A 105, 032416 (2022).

[69] J. Kaniewski, I. Supic, J, Tura, F. Baccari, A. Salavrakos, and R. Augusiak, Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems, Quantum 3, 198 (2019).

[70] W. N. Anderson, Jr., E. J. Harner, and G. E. Trapp, Eigenvalues of the difference and product of projections, Linear Multilinear Algebra 17, 295-299 (1985).

Cited by

[1] Subhankar Bera, Ananda G. Maity, Shiladitya Mal, and A. S. Majumdar, "Nonclassical temporal correlation powers quantum random access codes", arXiv:2204.05537.

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