Microwave quantum illumination

Physical Review Letters

Volumn 114, Issue 8, 2015, Pages

  Barzanjeh, Shabir ^a   Guha, Saikat ^b   Weedbrook, Christian ^c   Vitali, David ^d   Shapiro, Jeffrey H ^e   Pirandola, Stefano ^f  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b BBN TECHNOLOGIES   (United States)

^c QKD Corporation   (Canada)

^d UNIVERSITY OF CAMERINO   (Italy)

^e MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^f UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM ENTANGLEMENT; RADAR;

ERROR PROBABILITIES; MICROWAVE RADARS; MICROWAVE REGIME; MICROWAVE SIGNALS; NATURALLY OCCURRING; QUANTUM ILLUMINATIONS; QUANTUM MEASUREMENT; THERMAL BACKGROUND;

MICROWAVES;

EID: 84924079240     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.114.080503     Document Type: Article

References (49)

1. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
2. M.M. Wilde, Quantum Information Theory, (Cambridge University Press, Cambridge, England, 2013).
3. C. Weedbrook, S. Pirandola, R. García-Patrón, N.J. Cerf, T.C. Ralph, J.H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012). RMPHAT 0034-6861 10.1103/RevModPhys.84.621
4. S. Lloyd, Science 321, 1463 (2008). SCIEAS 0036-8075 10.1126/science.1160627
5. S.-H. Tan, B.I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J.H. Shapiro, Phys. Rev. Lett. 101, 253601 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.253601
6. S. Guha and B.I. Erkmen, Phys. Rev. A 80, 052310 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.80.052310
7. C. Weedbrook, S. Pirandola, J. Thompson, V. Vedral, and M. Gu, arXiv:1312.3332.
8. J.H. Shapiro, Phys. Rev. A 80, 022320 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.80.022320
9. Z. Zhang, M. Tengner, T. Zhong, F.N.C. Wong, and J.H. Shapiro, Phys. Rev. Lett. 111, 010501 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.010501
10. S. Pirandola, Phys. Rev. Lett. 106, 090504 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.090504
11. S. Pirandola, C. Lupo, V. Giovannetti, S. Mancini, and S.L. Braunstein, New J. Phys. 13, 113012 (2011). NJOPFM 1367-2630 10.1088/1367-2630/13/11/113012
12. G. Spedalieri, C. Lupo, S. Mancini, S.L. Braunstein, and S. Pirandola, Phys. Rev. A 86, 012315 (2012). PLRAAN 1050-2947 10.1103/PhysRevA.86.012315
13. C. Lupo, S. Pirandola, V. Giovannetti, and S. Mancini, Phys. Rev. A 87, 062310 (2013). PLRAAN 1050-2947 10.1103/PhysRevA.87.062310
14. E.D. Lopaeva, I. Ruo Berchera, I.P. Degiovanni, S. Olivares, G. Brida, and M. Genovese, Phys. Rev. Lett. 110, 153603 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.153603
15. Z. Zhang, S. Mouradian, F.N.C. Wong, and J.H. Shapiro, arXiv:1411.5969.
16. C. Weedbrook, S. Pirandola, S. Lloyd, and T.C. Ralph, Phys. Rev. Lett. 105, 110501 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.110501
17. C. Weedbrook, S. Pirandola, and T.C. Ralph, Phys. Rev. A 86, 022318 (2012). PLRAAN 1050-2947 10.1103/PhysRevA.86.022318
18. C. Weedbrook, C. Ottaviani, and S. Pirandola, Phys. Rev. A 89, 012309 (2014). PLRAAN 1050-2947 10.1103/PhysRevA.89.012309
19. Sh. Barzanjeh, D. Vitali, P. Tombesi, and G.J. Milburn, Phys. Rev. A 84, 042342 (2011). PLRAAN 1050-2947 10.1103/PhysRevA.84.042342
20. Sh. Barzanjeh, M. Abdi, G.J. Milburn, P. Tombesi, and D. Vitali, Phys. Rev. Lett. 109, 130503 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.130503
21. R.W. Andrews, R.W. Peterson, T.P. Purdy, K. Cicak, R.W. Simmonds, C.A. Regal, and K.W. Lehnert, Nat. Phys. 10, 321 (2014). NPAHAX 1745-2473 10.1038/nphys2911
22. J. Bochmann, A. Vainsencher, D.D. Awschalom, and A.N. Cleland, Nat. Phys. 9, 712 (2013). NPAHAX 1745-2473 10.1038/nphys2748
23. T. Bagci, A. Simonsen, S. Schmid, L.G. Villanueva, E. Zeuthen, J. Appel, J.M. Taylor, A. Sørensen, A. Schliesser, and E.S. Polzik, Nature (London) 507, 81 (2014). NATUAS 0028-0836 10.1038/nature13029
24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.114.080503, which includes Refs. [25-28]. We provide technical details on the following: (i) Hamiltonian of an electro-optomechanical system, (ii) linearization of the Hamiltonian, (iii) derivation of the quantum Langevin equations with internal losses, (iv) study of the microwave-optical entanglement considering the entanglement metric, the logarithmic negativity and the coherent information, (v) general study of the quantum correlations as quantified by quantum discord, and (vi) analysis of the error probability for (Equation presented) mode pairs.
25. I. Devetak and A. Winter, Proc. R. Soc. A 461, 207 (2005). PRLAAZ 1364-5021 10.1098/rspa.2004.1372
26. R. García-Patrón, S. Pirandola, S. Lloyd, and J.H. Shapiro, Phys. Rev. Lett. 102, 210501 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.210501
27. S. Pirandola, R. García-PatroÍn, S.L. Braunstein, and S. Lloyd, Phys. Rev. Lett. 102, 050503 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.050503
28. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012). RMPHAT 0034-6861 10.1103/RevModPhys.84.1655
29. T.A. Palomaki, J.D. Teufel, R.W. Simmonds, and K.W. Lehnert, Science 342, 710 (2013). SCIEAS 0036-8075 10.1126/science.1244563
30. S.G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, Phys. Rev. A 84, 052327 (2011). PLRAAN 1050-2947 10.1103/PhysRevA.84.052327
31. T.A. Palomaki, J.W. Harlow, J.D. Teufel, R.W. Simmonds, and K.W. Lehnert, Nature (London) 495, 210 (2013). NATUAS 0028-0836 10.1038/nature11915
32. The system is stable if the Routh-Hurwitz criterion is satisfied. For (Equation presented), this criterion reduces to the following necessary and sufficient condition [33]: κw Γw-κo Γo> K max{κw-κo, κo2-κw2 2γM+κw+κo }, where (Equation presented).
33. Y.-D. Wang and A.A. Clerk, Phys. Rev. Lett. 110, 253601 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.253601
34. J. Eisert, Ph.D. thesis, University of Potsdam, 2001;
35. G. Vidal and R.F. Werner, Phys. Rev. A 65, 032314 (2002); PLRAAN 1050-2947 10.1103/PhysRevA.65.032314
36. M.B. Plenio, Phys. Rev. Lett. 95, 090503 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.090503
37. B. Schumacher and M.A. Nielsen, Phys. Rev. A 54, 2629 (1996). PLRAAN 1050-2947 10.1103/PhysRevA.54.2629
38. S. Lloyd, Phys. Rev. A 55, 1613 (1997). PLRAAN 1050-2947 10.1103/PhysRevA.55.1613
39. S. Pirandola, G. Spedalieri, S.L. Braunstein, N.J. Cerf, and S. Lloyd, Phys. Rev. Lett. 113, 140405 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.140405
40. The common bandwidth of the entangled microwave and optical fields is (Equation presented), in terms of the resonator's damping rate and the cooperativity parameters.
41. K.M.R. Audenaert, J. Calsamiglia, R. Muñoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, Phys. Rev. Lett. 98, 160501 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.160501
42. K.M.R. Audenaert, M. Nussbaum, A. Szkola, and F. Verstraete, Commun. Math. Phys. 279, 251 (2008). CMPHAY 0010-3616 10.1007/s00220-008-0417-5
43. S. Pirandola and S. Lloyd, Phys. Rev. A 78, 012331 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.78.012331
44. A. Reiserer, S. Ritter, and G. Rempe, Science 342, 1349 (2013). SCIEAS 0036-8075 10.1126/science.1246164
45. M. Zhong, M.P. Hedges, R.L. Ahlefeldt, J.G. Bartholomew, S.E. Beavan, S.M. Wittig, J.J. Longdell, and M.J. Sellars, Nature (London) 517, 177 (2015). NATUAS 0028-0836 10.1038/nature14025
46. M.A. Castellanos-Beltran and K.W. Lehnert, Appl. Phys. Lett. 91, 083509 (2007). APPLAB 0003-6951 10.1063/1.2773988
47. N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V.E. Manucharyan, L. Frunzio, D.E. Prober, R.J. Schoelkopf, S.M. Girvin, and M.H. Devoret, Nature (London) 465, 64 (2010). NATUAS 0028-0836 10.1038/nature09035
48. N. Roch, E. Flurin, F. Nguyen, P. Morfin, P. Campagne-Ibarcq, M.H. Devoret, and B. Huard, Phys. Rev. Lett. 108, 147701 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.147701
49. C. Eichler, Y. Salathe, J. Mlynek, S. Schmidt, and A. Wallraff, Phys. Rev. Lett. 113, 110502 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.110502