Quantum state majorization at the output of bosonic gaussian channels

Nature Communications

Volumn 5, Issue , 2014, Pages

  Mari, A ^a   Giovannetti, V ^a   Holevo, A S ^b,c  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

GAUSSIAN METHOD; NOISE; OPTIMIZATION; PARTICLE MOTION; QUANTUM MECHANICS;

ARTICLE; ENVIRONMENT; NOISE; NORMAL DISTRIBUTION; QUANTUM COMMUNICATION THEORY; QUANTUM MECHANICS;

EID: 84900024188     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms4826     Document Type: Article

References (36)

1. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423 (1948).
2. Bennett, C. H. & Shor, P. W. Quantum information theory. IEEE Trans. Inf. Theory 44, 2724-2742 (1998).
3. Caves, C. M. & Drummond, P. B. Quantum limits on bosonic communication rates. Rev. Mod. Phys. 66, 481-537 (1994).
4. Holevo, A. S. Quantum systems, channels, information: A mathematical introduction (De Gruyter, 2012).
5. Holevo, A. S. & Werner, R. F. Evaluating capacities of bosonic Gaussian channels. Phys. Rev. A 63, 032312 (2001).
6. Holevo, A. S. The capacity of the quantum channel with general signal states. IEEE Trans. Inf. Theory 44, 269-273 (1998).
7. Braunstein, S. L. & van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513-577 (2005).
8. Weedbroock, C. et al. Gaussian Quantum Information. Rev. Mod. Phys. 84, 621-669 (2012).
9. Nielsen, M. A. & Vidal, G. Majorization and the interconversion of bipartite states. Quantum Inf. Comput. 1, 76-93 (2001).
10. Petz, D. Quantum Information Theory and Quantum Statistics (Springer, 2008).
11. Wehrl, A. General properties of entropy. Rev. Mod. Phys. 50, 221-260 (1978).
12. Carlen, E. Trace inequalities and quantum entropy. An introductory course. Contemp. Math. 529, 73-140 (2010).
13. Kaftal, V. & Weiss, G. An infinite dimensional Schur-Horn Theorem and majorization theory. J. Funct. Anal. 259, 3115-3162 (2010).
14. 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).
15. 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).
16. 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).
17. Wolf, M. M., Giedke, G., Krüger, O., Werner, R. F. & Cirac, J. I. Gaussian entanglement of formation. Phys. Rev. A 69, 052320 (2004).
18. Giovannetti, V., Garcia-Patron, R., Cerf, N. J. & Holevo, A. S. Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture. Preprint at http://arxiv.org/abs/1312.6225 (2013).
19. König, R. & Smith, G. Classical capacity of quantum thermal noise channels to within 1.45 Bits. Phys. Rev. Lett. 110, 040501 (2013).
20. König, R. & Smith, G. Limits on classical communication from quantum entropy power inequalities. Nat. Photon. 7, 142-146 (2013).
21. Giovannetti, V., Lloyd, S., Maccone, L. & Shapiro, J. H. Electromagnetic channel capacity for practical purposes. Nat. Photon. 7, 834-838 (2013).
22. Garća-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).
23. Giovannetti, V. & Lloyd, S. Additivity properties of a Gaussian channel. Phys. Rev. A 69, 032315 (2004).
24. 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, 032315 (2004).
25. Modi, K., Brodutch, A., Cable, H., Paterek, T. & Vedral, V. The classicalquantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655-1707 (2012).
26. Pirandola, S., Cerf, N. J., Braunstein, S. L. & Lloyd, S. Bosonic Minimum Output Entropy and Gaussian Discord. Preprint at http://arxiv.org/abs/ 1309.2215 (2013).
27. Giovannetti, V., Guha, S., Lloyd, S., Maccone, L. & Shapiro, J. H. Minimum bosonic channel output entropies. AIP Conf. Proc. 734, 21-24 (2004).
28. Serafini, A., Eisert, J. & Wolf, M. M. Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs. Phys. Rev. A 71, 012320 (2005).
29. 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).
30. 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).
31. Schäfer, J., Karpov, E., Garća-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).
32. Giovannetti, V., Holevo, A. S. & Garcia-Patron, R. A solution of the Gaussian optimizer conjecture. Preprint at http://arxiv.org/abs/1312.2251 (2013).
33. Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information (Cambridge University Press, 2000).
34. Aharonov, Y., Falkoff, D., Lerner, E. & Pendleton, H. A quantum characterization of classical radiation. Ann. Phys. 39, 498-512 (1966).
35. Asbóth, J. K., Calsamiglia, J. & Ritsch, H. Computable measure of nonclassicality for light. Phys. Rev. Lett. 94, 173602 (2005).
36. Jiang, Z., Lang, M. D. & Caves, C. M. Mixing nonclassical pure states in a linear-optical network almost always generates modal entanglement. Phys. Rev. A 88, 044301 (2013).