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Semi-device-independently characterizing quantum temporal correlations

Published 31 May 2023 in quant-ph | (2305.19548v3)

Abstract: We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device-independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signalling in time, there are upper bounds on the involved systems' dimensions, rank constraints -- for which we prove genuine quantum separations over local hidden variable models -- or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, bounding the maximum successful probability in quantum randomness access codes.

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References (56)
  1. J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics Physique Fizika 1, 195–200 (1964).
  2. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani,  and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
  3. 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).
  4. V. Scarani, “The device-independent outlook on quantum physics,” Acta Phys. Slovaca 62, 347–409 (2012).
  5. S. Pironio, A. Acín, S. Massar, A. B. de la 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, 1021–1024 (2010).
  6. Y.-C. Liang, D. Rosset, J.-D. Bancal, G. Pütz, T. J. Barnea,  and N. Gisin, “Family of Bell-like inequalities as device-independent witnesses for entanglement depth,” Phys. Rev. Lett. 114, 190401 (2015).
  7. F. Baccari, D. Cavalcanti, P. Wittek,  and A. Acín, “Efficient device-independent entanglement detection for multipartite systems,” Phys. Rev. X 7, 021042 (2017).
  8. T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann,  and O. Gühne, “Device-independent entanglement quantification and related applications,” Phys. Rev. Lett. 111, 030501 (2013).
  9. T. H. Yang, T. Vértesi, J.-D. Bancal, V. Scarani,  and M. Navascués, “Robust and versatile black-box certification of quantum devices,” Phys. Rev. Lett. 113, 040401 (2014).
  10. S.-L. Chen, C. Budroni, Y.-C. Liang,  and Y.-N. Chen, “Natural framework for device-independent quantification of quantum steerability, measurement incompatibility, and self-testing,” Phys. Rev. Lett. 116, 240401 (2016a).
  11. S.-L. Chen, C. Budroni, Y.-C. Liang,  and Y.-N. Chen, “Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations,” Phys. Rev. A 98, 042127 (2018).
  12. S.-L. Chen, N. Miklin, C. Budroni,  and Y.-N. Chen, “Device-independent quantification of measurement incompatibility,” Phys. Rev. Research 3, 023143 (2021a).
  13. M. Navascués, S. Pironio,  and A. Acín, “Bounding the set of quantum correlations,” Phys. Rev. Lett. 98, 010401 (2007).
  14. M. Navascués, S. Pironio,  and A. Acín, “A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations,” New J. Phys. 10, 073013 (2008).
  15. A. C. Doherty, Y.-C. Liang, B. Toner,  and S. Wehner, “The quantum moment problem and bounds on entangled multi-prover games,” in 23rd Annu. IEEE Conf. on Comput. Comp, 2008, CCC’08 (Los Alamitos, CA, 2008) pp. 199–210.
  16. A. C. Doherty, P. A. Parrilo,  and F. M. Spedalieri, “Complete family of separability criteria,” Phys. Rev. A 69, 022308 (2004).
  17. J. Eisert, P. Hyllus, O. Gühne,  and M. Curty, “Complete hierarchies of efficient approximations to problems in entanglement theory,” Phys. Rev. A 70, 062317 (2004).
  18. C. Emary, N. Lambert,  and F. Nori, “Leggett-Garg inequalities,” Rep. Prof. Phys. 77, 016001 (2013).
  19. G. Vitagliano and C. Budroni, “Leggett-Garg macrorealism and temporal correlations,”  (2022), arXiv:2212.11616 .
  20. A. J. Leggett and A. Garg, “Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?” Phys. Rev. Lett. 54, 857–860 (1985).
  21. T. Fritz, “Quantum correlations in the temporal Clauser–Horne–Shimony–Holt (CHSH) scenario,” New J. Phys. 12, 083055 (2010).
  22. C. Budroni, T. Moroder, M. Kleinmann,  and O. Gühne, “Bounding temporal quantum correlations,” Phys. Rev. Lett. 111, 020403 (2013).
  23. S. Boyd and L. Vandenberghe, Convex optimization, 1st ed. (Cambridge University Press, Cambridge, 2004).
  24. B. Lang, T. Vértesi,  and M. Navascués, “Closed sets of correlations: answers from the zoo,” J. Phys. A 47, 424029 (2014).
  25. M. Berta, O. Fawzi,  and V. B. Scholz, “Quantum bi-linear optimization,” SIAM J. Opt. 26, 1529–1564 (2016).
  26. J. Bowles, F. Baccari,  and A. Salavrakos, “Bounding sets of sequential quantum correlations and device-independent randomness certification,” Quantum 4, 344 (2020).
  27. P.-S. Lin, T. Vértesi,  and Y.-C. Liang, “Naturally restricted subsets of nonsignaling correlations: typicality and convergence,” Quantum 6, 765 (2022).
  28. Y.-C. Liang, T. Vértesi,  and N. Brunner, “Semi-device-independent bounds on entanglement,” Phys. Rev. A 83, 022108 (2011).
  29. I. Roth, J. Wilkens, D. Hangleiter,  and J. Eisert, “Semi-device-dependent blind quantum tomography,” Quantum  (2023), arXiv:2006.03069.
  30. L. Clemente and J. Kofler, “No fine theorem for macrorealism: Limitations of the Leggett-Garg inequality,” Phys. Rev. Lett. 116, 150401 (2016).
  31. S. Brierley, A. Kosowski, M. Markiewicz, T. Paterek,  and A. Przysiężna, “Nonclassicality of temporal correlations,” Phys. Rev. Lett. 115, 120404 (2015).
  32. M. Navascués and T. Vértesi, “Bounding the set of finite dimensional quantum correlations,” Phys. Rev. Lett. 115, 020501 (2015).
  33. R. Gallego, N. Brunner, C. Hadley,  and A. Acín, “Device-independent tests of classical and quantum dimensions,” Phys. Rev. Lett. 105, 230501 (2010).
  34. J. F. Clauser, M. A. Horne, A. Shimony,  and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880–884 (1969).
  35. F. De Zela, “Single-qubit tests of Bell-like inequalities,” Phys. Rev. A 76, 042119 (2007).
  36. J. Hoffmann, C. Spee, O. Gühne,  and C. Budroni, “Structure of temporal correlations of a qubit,” New J. Phys. 20, 102001 (2018).
  37. B. S. Cirel’son, “Quantum generalizations of Bell’s inequality,” Lett. in Math. Phys. 4, 93–100 (1980).
  38. Y.-N. Chen, C.-M. Li, N. Lambert, S.-L. Chen, Y. Ota, G.-Y. Chen,  and F. Nori, “Temporal steering inequality,” Phys. Rev. A 89, 032112 (2014).
  39. E. G. Cavalcanti, S. J. Jones, H. M. Wiseman,  and M. D. Reid, “Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox,” Phys. Rev. A 80, 032112 (2009).
  40. S.-L. Chen, N. Lambert, C.-M. Li, A. Miranowicz, Y.-N. Chen,  and F. Nori, “Quantifying non-Markovianity with temporal steering,” Phys. Rev. Lett. 116, 020503 (2016b).
  41. S.-L. Chen, N. Lambert, C.-M. Li, G.-Y. Chen, Y.-N. Chen, A. Miranowicz,  and F. Nori, “Spatio-temporal steering for testing nonclassical correlations in quantum networks,” Sci. Rep. 7, 3728 (2017).
  42. C.-M. Li, Y.-N. Chen, N. Lambert, C.-Y. Chiu,  and F. Nori, “Certifying single-system steering for quantum-information processing,” Phys. Rev. A 92, 062310 (2015).
  43. H. M. Wiseman, S. J. Jones,  and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).
  44. R. Uola, F. Lever, O. Gühne,  and J.-P. Pellonpää, “Unified picture for spatial, temporal, and channel steering,” Phys. Rev. A 97, 032301 (2018).
  45. H.-Y. Ku, S.-L. Chen, H.-B. Chen, N. Lambert, Y.-N. Chen,  and F. Nori, “Temporal steering in four dimensions with applications to coupled qubits and magnetoreception,” Phys. Rev. A 94, 062126 (2016).
  46. A. Tavakoli, J. Kaniewski, T. Vértesi, D. Rosset,  and N. Brunner, “Self-testing quantum states and measurements in the prepare-and-measure scenario,” Phys. Rev. A 98, 062307 (2018).
  47. S.-H. Wei, F.-Z. Guo, X.-H. Li,  and Q.-Y. Wen, “Robustness self-testing of states and measurements in the prepare-and-measure scenario with 3→1→313\rightarrow 13 → 1 random access code,” Chinese Phys. B 28, 070304 (2019).
  48. N. Miklin and M. Oszmaniec, “A universal scheme for robust self-testing in the prepare-and-measure scenario,” Quantum 5, 424 (2021).
  49. I. Šupić and J. Bowles, “Self-testing of quantum systems: a review,” Quantum 4, 337 (2020).
  50. Y.-C. Liang, Y.-H. Yeh, P. E. M. F. Mendonça, R. Y. Teh, M. D. Reid,  and P. D. Drummond, “Quantum fidelity measures for mixed states,” Rep. Prof. Phys. 82, 076001 (2019).
  51. A. Uhlmann, “The “transition probability” in the state space of a ∗∗\ast∗-algebra,” Rep. Math. Phys. 9, 273–279 (1976).
  52. R. Jozsa, “Fidelity for mixed quantum states,” J. Mod. Opt. 41, 2315–2323 (1994).
  53. S.-L. Chen, H.-Y. Ku, W. Zhou, J. Tura,  and Y.-N. Chen, “Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification,” Quantum 5, 552 (2021b).
  54. C.-C. Lien and S.-L. Chen,  (2023), in preparation.
  55. We omit the superscripts representing the Hilbert spaces the operators acting on when there is no risk of confusion.
  56. A. Peres, “Neumark’s theorem and quantum inseparability,” Found Phys. 20, 1441–1453 (1990).
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Authors (2)

  1. Shin-Liang Chen 
  2. Jens Eisert 

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