Continuous Time Classical Capacity of Quantum Channel

References

1. Gordon, J. P. Quantum effects in communications systems. Proc. IRE 1898–1908 (1962).

2. Caves, C. M. & Drummond, P. B. Quantum limits on bosonic communication rates. Rev. Mod. Phys. 66, 481–537 (1994).

   Article  ADS  Google Scholar

3. Schumacher, B. & Westmoreland, W. D. Sending classical information via noisy quantum channels. Phys. Rev. A 56, 131–138 (1997).

   Article  ADS  Google Scholar

4. Holevo, A. S. The capacity of the quantum channel with general signal states. IEEE Trans. Inf. Theory 44, 269–273 (1998).

   Article  MathSciNet  Google Scholar

5. Bennett, C. H. & Shor, P. W. Quantum information theory. IEEE Trans. Inf. Theory 44, 2724–2742 (1998).

   Article  MathSciNet  Google Scholar

6. Holevo, A. S. & Werner, R. F. Evaluating capacities of bosonic Gaussian channels. Phys. Rev. A 63, 032312 (2001).

   Article  ADS  Google Scholar

7. Giovannetti, V., Guha, S., Lloyd, S., Maccone, L. & Shapiro, J. H. Minimum output entropy of bosonic channels: a conjecture. Phys. Rev. A 70, 032315 (2004).

   Article  ADS  Google Scholar

8. Giovannetti, V., Guha, S., Lloyd, S., Maccone, L. & Shapiro, J. H. Minimum bosonic channel output entropies. AIP Conf. Proc. 734, 21–24 (2004).

   Article  ADS  Google Scholar

9. Giovannetti, V., Holevo, A. S., Lloyd, S. & Maccone, L. Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results. J. Phys. A 43, 415305 (2010).

   Article  MathSciNet  Google Scholar

10. García-Patrón, R., Navarrete-Benlloch, C., Lloyd, S., Shapiro, J. H. & Cerf, N. J. Majorization theory approach to the Gaussian channel minimum entropy conjecture. Phys. Rev. Lett. 108, 110505 (2012).

    Article  ADS  Google Scholar

11. García-Patrón, R., Navarrete-Benlloch, C., Lloyd, S., Shapiro, J. H. & Cerf, N. J. The holy grail of quantum optical communication. in Proc. 11th International Conference on Quantum Communication, Measurement and Computing, 68 (2012).

12. Weedbrook, C. et al. Gaussian quantum information. Rev. Mod. Phys. 84, 621–669 (2012).

    Article  ADS  Google Scholar

13. König, R. & Smith, G. Classical capacity of quantum thermal noise channels to within 1.45 bits. Phys. Rev. Lett. 110, 040501 (2013).

    Article  ADS  Google Scholar

14. König, R. & Smith, G. Limits on classical communication from quantum entropy power inequalities. Nature Photon. 7, 142–146 (2013).

    Article  ADS  Google Scholar

15. Giovannetti, V., Lloyd, S., Maccone, L. & Shapiro, J. H. Electromagnetic channel capacity for practical purposes. Nature Photon. 7, 834–838 (2013).

    Article  ADS  Google Scholar

16. Giovannetti, V. & Lloyd, S. Additivity properties of a Gaussian channel. Phys. Rev. A 69, 062307 (2004).

    Article  ADS  MathSciNet  Google Scholar

17. Giovannetti, V., Lloyd, S., Maccone, L., Shapiro, J. H. & Yen, B. J. Minimum Rényi and Wehrl entropies at the output of bosonic channels. Phys. Rev. A 70, 022328 (2004).

    Article  ADS  MathSciNet  Google Scholar

18. Serafini, A., Eisert, J. & Wolf, M. M. Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs. Phys. Rev. A 71, 012320 (2005).

    Article  ADS  Google Scholar

19. Guha, S., Shapiro, J. H. & Erkmen, B. I. Classical capacity of bosonic broadcast communication and a minimum output entropy conjecture. Phys. Rev. A 76, 032303 (2007).

    Article  ADS  Google Scholar

20. Giovannetti, V., Holevo, A. S. & García-Patrón, R. A solution of the Gaussian optimizer conjecture. Preprint at http://arxiv.org/abs/1312.2251 (2013).

21. Bennett, C. H., DiVincenzo, D. P., Smolin, J. A. & Wootters, W. K. Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 (1996).

    Article  ADS  MathSciNet  Google Scholar

22. Modi, K., Brodutch, A., Cable, H., Paterek, T. & Vedral, V. The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012).

    Article  ADS  Google Scholar

23. Pirandola, S., Spedalieri, G., Braunstein, S. L., Cerf, N. J. & Lloyd, S. Optimality of Gaussian discord. Preprint at http://arxiv.org/abs/1309.2215v2 (2014).

24. Cover, T. M. & Thomas, J. A. Elements of Information Theory (Wiley, 1968).

    MATH  Google Scholar

25. Holevo, A. S. Quantum Systems, Channels, Information. A Mathematical Introduction (De Gruyter, 2012).

    Book  Google Scholar

26. Braunstein, S. L. & van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005).

    Article  ADS  MathSciNet  Google Scholar

27. Cerf, N. J., Leuchs, G. & Polzik, E. S. (eds) Quantum Information with Continuous Variables of Atoms and Light (Imperial College Press, 2007).

    Book  Google Scholar

28. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer, 1994).

    Book  Google Scholar

29. Schäfer, J., Karpov, E., García-Patrón, R., Pilyavets, O. V. & Cerf, N. J. Equivalence relations for the classical capacity of single-mode Gaussian quantum channels. Phys. Rev. Lett. 111, 030503 (2013).

    Article  ADS  Google Scholar

30. Caruso, F. & Giovannetti, V. Degradability of bosonic Gaussian channels. Phys. Rev. A 74, 062307 (2006).

    Article  ADS  Google Scholar

31. Holevo, A. S. One-mode quantum Gaussian channels: structure and quantum capacity. Probl. Inf. Transm. 43, 1–11 (2007).

    Article  MathSciNet  Google Scholar

32. Caruso, F., Giovannetti, V. & Holevo, A. S. One-mode bosonic Gaussian channels: a full weak-degradability classification. New J. Phys. 8, 310 (2006).

    Article  ADS  Google Scholar

33. Giovannetti, V. et al. Classical capacity of the lossy bosonic channel: the exact solution. Phys. Rev. Lett. 92, 027902 (2004).

    Article  ADS  Google Scholar

34. Holevo, A. S. Quantum coding theorems. Russ. Math. Surveys 53, 1295–1331 (1998).

    Article  ADS  MathSciNet  Google Scholar

35. Holevo, A. S. & Shirokov, M. E. Continuous ensembles and the χ-capacity of infinite-dimensional channels. Theory Prob. Appl. 50, 86–98 (2006).

    Article  MathSciNet  Google Scholar

36. Wehrl, A. General properties of entropy. Rev. Mod. Phys. 50, 221–260 (1978).

    Article  ADS  MathSciNet  Google Scholar

37. Holevo, A. S. Complementary channels and the additivity problem. Theory Prob. Appl. 51, 92–100 (2007).

    Article  MathSciNet  Google Scholar

38. King, C., Matsumoto, K., Natanson, M. & Ruskai, M. B. Properties of conjugate channels with applications to additivity and multiplicativity. Markov Process. Relat. Fields 13, 391–423 (2007).

    MathSciNet  MATH  Google Scholar

39. Holevo, A. S. Entanglement-breaking channels in infinite dimensions. Probl. Inf. Transm. 44, 171–184 (2008).

    Article  MathSciNet  Google Scholar

40. Lupo, C., Pilyavets, O. V. & Mancini, S. Capacities of lossy bosonic channel with correlated noise. New J. Phys. 11, 063023 (2009).

    Article  ADS  Google Scholar

41. Giedke, G., Wolf, M. M., Krüger, O., Werner, R. F. & Cirac, J. I. Entanglement of formation for symmetric Gaussian states. Phys. Rev. Lett. 91, 107901 (2003).

    Article  ADS  Google Scholar

42. Wolf, M. M., Giedke, G., Krüger, O., Werner, R. F. & Cirac, J. I. Gaussian entanglement of formation. Phys. Rev. A 69, 052320 (2004).

    Article  ADS  Google Scholar

43. Matsumoto, K., Shimono, T. & Winter, A. Remarks on additivity of the Holevo channel capacity and of the entanglement of formation. Commun. Math. Phys. 246, 427–442 (2004).

    Article  ADS  MathSciNet  Google Scholar

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Acknowledgements

The authors thank L. Ambrosio, A. Mari, C. Navarrete-Benloch, J. Oppenheim, M.E. Shirokov, R.F. Werner and A. Winter for comments and discussions. The authors acknowledge support and the catalysing role of the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; an important part of this work was conducted when attending the Newton Institute programme 'Mathematical Challenges in Quantum Information'. A.H. acknowledges the Rothschild Distinguished Visiting Fellowship, which enabled him to participate in the programme, and partial support from RAS Fundamental Research Programs (the Russian Quantum Center). N.J.C. and R.G.-P. acknowledge financial support from the Belgian Fonds de la Recherche Scientifique (F.R.S.–FNRS) under projects T.0199.13 and HIPERCOM (High-Performance Coherent Quantum Communications), as well as from the 'Interuniversity Attraction Poles' programme of the Belgian Science Policy Office (grant no. IAP P7-35 Photonics@be). R.G.-P. acknowledges financial support from the Alexander von Humboldt Foundation, the F.R.S.–FNRS and Back-to-Belgium grant from the Belgian Federal Science Policy.

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Authors and Affiliations

1. NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Pisa, I-56127, Italy

   V. Giovannetti

2. QuIC, Ecole Polytechnique de Bruxelles, CP 165, Université Libre de Bruxelles, Bruxelles, 1050, Belgium

   R. García-Patrón & N. J. Cerf

3. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748, Germany

   R. García-Patrón

4. Steklov Mathematical Institute, RAS, 119991 Moscow, Russia

   A. S. Holevo

5. National Research University Higher School of Economics (HSE), Moscow, 101000, Russia

   A. S. Holevo

Contributions

All authors contributed equally to the research and writing of the manuscript.

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Correspondence to V. Giovannetti.

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The authors declare no competing financial interests.

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Giovannetti, V., García-Patrón, R., Cerf, N. et al. Ultimate classical communication rates of quantum optical channels. Nature Photon 8, 796–800 (2014). https://doi.org/10.1038/nphoton.2014.216

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• Received: 30 January 2014

• Accepted: 14 August 2014

• Published: 21 September 2014

• Issue Date: October 2014

• DOI : https://doi.org/10.1038/nphoton.2014.216

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Source: https://www.nature.com/articles/nphoton.2014.216

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