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Entropic uncertainty relations and entanglement detection from quantum designs (2312.09765v1)

Published 15 Dec 2023 in quant-ph

Abstract: Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information theory. In this article, we investigate entropic uncertainty relations and entanglement detection with an emphasis on quantum measurements with design structures. On the one hand, we derive improved R\'enyi entropic uncertainty relations for design-structured measurements, exploiting the property that the sum of powered (e.g., squared) probabilities of obtaining different measurement outcomes is now invariant under unitary transformations of the measured system and can be easily computed. On the other hand, the above property essentially imposes a state-independent upper bound, which is achieved at all pure states, on one's ability to predict local outcomes when performing a set of design-structured measurements on quantum systems. Realizing this, we also obtain criteria for detecting multi-partite entanglement with design-structured measurements.

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References (57)
  1. Quantum 3, 133 (2019).
  2. J. Phys. A: Math. Theor. 54, 225301 (2021).
  3. I. Ivonovic, J. Phys. A: Math. Gen. 14, 3241 (1981).
  4. W. K. Wootters and B. D. Fields, Ann. Phys. 191, 363 (1989).
  5. A. O. Pittenger and M. H. Rubin, Linear Algebra Appl. 390, 255 (2004).
  6. Int. J. Quantum Inform. 08, 535 (2010).
  7. New J. Phys. 16, 053038 (2014).
  8. Quantum Inf. Process. 20, 401 (2021).
  9. IEEE Trans. Inform. Theory 69, 3814 (2023).
  10. J. Math. Phys. 45, 2171 (2004).
  11. A. J. Scott and M. Grassl, J. Math. Phys. 51, 042203 (2010).
  12. J. Phys. A: Math. Theor. 47, 335302 (2014).
  13. Phys. Rev. A 86, 022311 (2012).
  14. A. E. Rastegin, Open Syst. Inf. Dyn. 22, 1550005 (2015).
  15. arXiv:2210.00958.
  16. Quantum Inf Process 15, 5119 (2016).
  17. W. K. Wootters, B. D. Fields, Ann. Phys. 191, 363–381 (1989).
  18. R. B. A. Adamson, A. M. Steinberg, Phys. Rev. Lett. 105, 030406 (2010).
  19. J. Math. Phys. 43, 4537–4559 (2002).
  20. Phys. Rev. Lett. 88, 127902 (2002).
  21. Phys. Rev. A 78, 012344 (2008).
  22. Quantum 2, 111 (2018).
  23. W. Heisenberg, Z. Phys. 43, 172 (1927).
  24. Commun.Math. Phys. 44, 129 (1975).
  25. D. Deutsch, Phys. Rev. Lett. 50, 631 (1983).
  26. H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988).
  27. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
  28. New J. Phys. 12, 025009 (2010).
  29. Rev. Mod. Phys. 89, 015002 (2017).
  30. Rev. Mod. Phys. 74, 145 (2002).
  31. IEEE Trans. Inf. Theory 58, 1962 (2012).
  32. IEEE Trans. Inf. Theory 61, 1093 (2015).
  33. U. Larsen, J. Phys. A: Math. Gen. 23, 1041 (1990).
  34. I. D. Ivanovic, J. Phys. A: Math. Gen. 25, L363 (1992).
  35. M. A. Ballester and S. Wehner, Phys. Rev. A 75, 022319 (2007).
  36. Phys. Rev. A 91, 042133 (2015).
  37. Phys. Rev. A 104, 062204 (2021).
  38. J. Sánchez-Ruiz, Phys. Lett. A 201, 125 (1995).
  39. Phys. Rev. A 79, 022104 (2009).
  40. A. E. Rastegin, Eur. Phys. J. D 67, 269(2013).
  41. Quantum Inf. Proc. 14, 2227 (2015).
  42. Phys. Rev. A 103, 042205 (2021).
  43. A. E. Rastegin, Proc. R. Soc. A 479, 20220546 (2023).
  44. arXiv:2309.16955.
  45. Phys. Rev. Research 2, 023130 (2020).
  46. A. E. Rastegin, J. Phys. A: Math. Theor. 53, 405301 (2020).
  47. A. Rényi, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, CA, 1961), Vol. 1, pp. 547.
  48. A. Haar, Ann. Math. 34, 147 (1933).
  49. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
  50. Phys. Rev. Lett. 68, 557 (1992).
  51. Phys. Rev. Lett. 108, 130503 (2012).
  52. Nature 464, 1021 (2010).
  53. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
  54. Phys. Rev. A 70, 022316 (2004).
  55. Phys. Rev. A 98, 062111 (2018).
  56. I. Bengtsson, AIP Conf. Proc. 889, 40(2007).
  57. M.-D. Choi, Linear Algebra Appl. 10, 285 (1975).

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