- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Open Access

Operational resource theory of quantum channels

Yunchao Liu1,2 and Xiao Yuan3,*

  • 1Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA
  • 2Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
  • 3Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom

  • *xiao.yuan.ph@gmail.com
PDF

Phys. Rev. Research 2, 012035(R) – Published 11 February, 2020

DOI: https://doi.org/10.1103/PhysRevResearch.2.012035

Abstract

Quantum resource theories have been widely studied to systematically characterize the nonclassicality of quantum systems. Most resource theories focus on quantum states and study their interconversions. Although quantum channels are generally used as a tool for state manipulation, such a manipulation capability can be naturally regarded as a generalized quantum resource, leading to an open research direction in the resource theories of quantum channels. Various resource-theoretic properties of the channels have been investigated, however, without treating the channels themselves as operational resources that can also be manipulated and converted. In this Rapid Communication, we address this problem by first proposing a general resource framework for quantum channels and introducing resource monotones based on general distance quantifiers of the channels. We study the interplay between the channel and state resource theories by relating the resource monotones of a quantum channel to its manipulation power of the state resource. Regarding channels as operational resources, we introduce asymptotic channel distillation and dilution, the most important tasks in an operational resource theory, and show how to bound the conversion rates with the channel resource monotones. Finally, we apply our results to quantum coherence as an example and introduce the coherence of channels, which characterizes the coherence generation ability of channels. We consider asymptotic channel distillation and dilution with maximally incoherent operations and find the theory asymptotically irreversible, in contrast to the asymptotic reversibility of the coherence of states.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (82)

  1. J. Aberg, arXiv:quant-ph/0612146.
  2. T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
  3. A. Streltsov, G. Adesso, and M. B. Plenio, Rev. Mod. Phys. 89, 041003 (2017).
  4. L. Henderson and V. Vedral, J. Phys. A: Math. Gen. 34, 6899 (2001).
  5. H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001).
  6. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
  7. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).
  8. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Phys. Rev. Lett. 78, 2275 (1997).
  9. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
  10. F. G. S. L. Brandão, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Phys. Rev. Lett. 111, 250404 (2013).
  11. J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, J. Phys. A: Math. Theor. 49, 143001 (2016).
  12. V. Veitch, C. Ferrie, D. Gross, and J. Emerson, New J. Phys. 14, 113011 (2012).
  13. V. Veitch, S. H. Mousavian, D. Gottesman, and J. Emerson, New J. Phys. 16, 013009 (2014).
  14. M. Howard and E. Campbell, Phys. Rev. Lett. 118, 090501 (2017).
  15. I. Devetak and A. Winter, Proc. R. Soc. A 461, 207 (2005).
  16. P. J. Coles, E. M. Metodiev, and N. Lütkenhaus, Nat. Commun. 7, 11712 (2016).
  17. X. Yuan, H. Zhou, Z. Cao, and X. Ma, Phys. Rev. A 92, 022124 (2015).
  18. X. Yuan, Q. Zhao, D. Girolami, and X. Ma, Adv. Quantum Technol. 2, 1900053 (2019).
  19. M. Hayashi and H. Zhu, Phys. Rev. A 97, 012302 (2018).
  20. N. Datta, IEEE Trans. Inf. Theory 55, 2816 (2009).
  21. S. Bravyi, G. Smith, and J. A. Smolin, Phys. Rev. X 6, 021043 (2016).
  22. M. Howard, J. Wallman, V. Veitch, and J. Emerson, Nature (London) 510, 351 (2014).
  23. M. Hillery, Phys. Rev. A 93, 012111 (2016).
  24. N. Anand and A. K. Pati, arXiv:1611.04542.
  25. E. Chitambar and G. Gour, Rev. Mod. Phys. 91, 025001 (2019).
  26. E. M. Rains, IEEE Trans. Inf. Theory 47, 2921 (2001).
  27. P. M. Hayden, M. Horodecki, and B. M. Terhal, J. Phys. A: Math. Gen. 34, 6891 (2001).
  28. A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 (2016).
  29. F. Buscemi and N. Datta, J. Math. Phys. 51, 102201 (2010).
  30. F. G. S. L. Brandao and N. Datta, IEEE Trans. Inf. Theory 57, 1754 (2011).
  31. F. Buscemi and N. Datta, Phys. Rev. Lett. 106, 130503 (2011).
  32. Q. Zhao, Y. Liu, X. Yuan, E. Chitambar, and X. Ma, Phys. Rev. Lett. 120, 070403 (2018).
  33. B. Regula, K. Fang, X. Wang, and G. Adesso, Phys. Rev. Lett. 121, 010401 (2018).
  34. Q. Zhao, Y. Liu, X. Yuan, E. Chitambar, and A. Winter, IEEE Trans. Inf. Theory 65, 6441 (2019).
  35. Z.-W. Liu, K. Bu, and R. Takagi, Phys. Rev. Lett. 123, 020401 (2019).
  36. M. Berta, F. G. S. L. Brandão, M. Christandl, and S. Wehner, IEEE Trans. Inf. Theory 59, 6779 (2013).
  37. S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Nat. Commun. 8, 15043 (2017).
  38. M. M. Wilde, Phys. Rev. A 98, 042338 (2018).
  39. K. Ben Dana, M. García Díaz, M. Mejatty, and A. Winter, Phys. Rev. A 95, 062327 (2017).
  40. M. G. Díaz, K. Fang, X. Wang, M. Rosati, M. Skotiniotis, J. Calsamiglia, and A. Winter, Quantum 2, 100 (2018).
  41. Á. Rivas and M. Müller, New J. Phys. 17, 062001 (2015).
  42. L. Li, K. Bu, and Z.-W. Liu, arXiv:1812.02572.
  43. R. Takagi and B. Regula, Phys. Rev. X 9, 031053 (2019).
  44. J. R. Seddon and E. Campbell, Proc. R. Soc. A 475, 20190251 (2019).
  45. X. Wang, M. M. Wilde, and Y. Su, New J. Phys. 21, 103002 (2019).
  46. C. H. Bennett, A. W. Harrow, D. W. Leung, and J. A. Smolin, IEEE Trans. Inf. Theory 49, 1895 (2003).
  47. E. Kaur and M. M. Wilde, J. Phys. A: Math. Theor. 51, 035303 (2017).
  48. S. Pirandola and C. Lupo, Phys. Rev. Lett. 118, 100502 (2017).
  49. M. Berta, C. Hirche, E. Kaur, and M. M. Wilde, arXiv:1808.01498.
  50. S. Pirandola, R. Laurenza, C. Lupo, and J. L. Pereira, npj Quantum Inf. 5, 50 (2019).
  51. D. Rosset, F. Buscemi, and Y.-C. Liang, Phys. Rev. X 8, 021033 (2018).
  52. T. Simnacher, N. Wyderka, C. Spee, X.-D. Yu, and O. Gühne, Phys. Rev. A 99, 062319 (2019).
  53. X. Yuan, Y. Liu, Q. Zhao, B. Regula, J. Thompson, and M. Gu, arXiv:1907.02521.
  54. Q. Zhuang, P. W. Shor, and J. H. Shapiro, Phys. Rev. A 97, 052317 (2018).
  55. J.-H. Hsieh, S.-H. Chen, and C.-M. Li, Sci. Rep. 7, 13588 (2017).
  56. S.-H. Chen, H. Lu, Q.-C. Sun, Q. Zhang, Y.-A. Chen, and C.-M. Li, Phys. Rev. Research 2, 013043 (2020).
  57. C.-C. Kuo, S.-H. Chen, W.-T. Lee, H.-M. Chen, H. Lu, and C.-M. Li, Sci. Rep. 9, 20316 (2019).
  58. E. Wolfe, D. Schmid, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, arXiv:1903.06311.
  59. B. Coecke, T. Fritz, and R. W. Spekkens, Inf. Comput. 250, 59 (2016).
  60. T. Theurer, D. Egloff, L. Zhang, and M. B. Plenio, Phys. Rev. Lett. 122, 190405 (2019).
  61. T. Cooney, M. Mosonyi, and M. M. Wilde, Commun. Math. Phys. 344, 797 (2016).
  62. F. Leditzky, E. Kaur, N. Datta, and M. M. Wilde, Phys. Rev. A 97, 012332 (2018).
  63. X. Yuan, Phys. Rev. A 99, 032317 (2019).
  64. G. Gour and M. M. Wilde, arXiv:1808.06980.
  65. G. Chiribella, G. M. D'Ariano, and P. Perinotti, Europhys. Lett. 83, 30004 (2008).
  66. D. Aharonov, A. Kitaev, and N. Nisan, in Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, STOC '98 (ACM, New York, 1998), pp. 20–30.
  67. J. Watrous, Theory Comput. 5, 217 (2009).
  68. A. Mani and V. Karimipour, Phys. Rev. A 92, 032331 (2015).
  69. M. García-Díaz, D. Egloff, and M. B. Plenio, Quantum Inf. Comput. 16, 1282 (2016).
  70. P. Zanardi, G. Styliaris, and L. Campos Venuti, Phys. Rev. A 95, 052307 (2017).
  71. P. Zanardi, G. Styliaris, and L. Campos Venuti, Phys. Rev. A 95, 052306 (2017).
  72. K. Bu, A. Kumar, L. Zhang, and J. Wu, Phys. Lett. A 381, 1670 (2017).
  73. M. Navascués and L. P. García-Pintos, Phys. Rev. Lett. 115, 010405 (2015).
  74. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.2.012035 for detailed proofs.
  75. F. G. Brandao and M. B. Plenio, Nat. Phys. 4, 873 (2008).
  76. F. G. S. L. Brandão and M. B. Plenio, Commun. Math. Phys. 295, 829 (2010).
  77. F. G. S. L. Brandão and G. Gour, Phys. Rev. Lett. 115, 070503 (2015).
  78. G. Gour and A. Winter, Phys. Rev. Lett. 123, 150401 (2019).
  79. Z.-W. Liu, X. Hu, and S. Lloyd, Phys. Rev. Lett. 118, 060502 (2017).
  80. F. G. S. L. Brandão and M. B. Plenio, Commun. Math. Phys. 295, 791 (2010).
  81. G. Gour, IEEE Trans. Inf. Theory 65, 5880 (2019).
  82. Z.-W. Liu and A. Winter, arXiv:1904.04201.

Outline

Information

Phys. Rev. Research 2, 012035(R)– Published 11 February, 2020
  • Received 19 May 2019
  • Accepted 7 January 2020
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation