Single-particle entanglement

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 72, Issue 6, 2005, Pages

  Van Enk, S J ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HIGH ENERGY PHYSICS;

SINGLE-PARTICLE ENTANGLEMENT;

ELEMENTARY PARTICLES;

EID: 33244466053     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.72.064306     Document Type: Article

References (31)

1. M. Pawlowski and M. Czachor, quant-ph/0507151, and references therein.
2. A. I. Lvovsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87. 050402 87, 050402 (2001);
3. G. Björk, P. Jonsson, and L. L. Sanchez Soto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.042106 64, 042106 (2001);
4. E. Lombardi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88. 070402 88, 070402 (2002);
5. J. W. Lee, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012324 68, 012324 (2003);
6. B. Hessmo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 180401 92, 180401 (2004);
7. S. A. Babichev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 193601 92, 193601 (2004).
8. This argument is not new: it appears in C. C. Gerry, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.4583 53, 4583 (1996).
9. Also, M. S. Kim has used this argument in the same way [M. S. Kim (private communication)]. See also Ref..
10. Y. Aharonov and L. Vaidman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.052108 61, 052108 (2000).
11. The qualification that the modes be spatially separated is important, and in certain cases absolutely crucial. This should be clear from the argument presented here, but also from S. J. van Enk, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022303 67, 022303 (2003);
12. see also P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65. 042101 65, 042101 (2002);
13. Y. Shi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.024301 67, 024301 (2003);
14. and for a generalized and more technical notion of what is important for entanglement, see H. Barnum, quant-ph/0305023;
15. quant-ph/0506099.
16. J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78. 3221 78, 3221 (1997). Actually, how one does this precisely, or whether one can achieve this perfectly experimentally at the present moment is not relevant.
17. Famously, because the original EPR [A. Einstein, B. Podolski, and N. Rosen, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.47.777 47, 777 (1935)] state is equivalent to an infinitely squeezed two-mode squeezed state.
18. The two-mode squeezed state for general (finite) squeezing parameter r is [D. Walls and G. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994)]
19. 1 cosh r n=0 (tanh r)nn. The entanglement in this state is [S. J. van Enk, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.5095 60, 5095 (1999)] E= cosh2 r log2 (cosh2 r) - sinh2 r log2 (sinh2 r).
20. H. M. Wiseman and J. A. Vaccaro, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.097902 91, 097902 (2003).
21. As shown in Ref. there is entanglement in two (or more) copies of the same state 4; see also S. J. van Enk, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032339 71, 032339 (2005). This demonstrates the asymmetry in the roles the state 4 and the reference frame play: although both seem to be needed to demonstrate entanglement, the entanglement can be said to arise from the state 4, not from the reference frame.
22. S. J. van Enk, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340110065763 48, 2049 (2001) pointed out the importance of a shared reference frame for teleportation, but see Ref. for an important exception.
23. S. D. Bartlett, T. Rudolph, and R. W. Spekkens, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.027901 91, 027901 (2003).
24. S. M. Tan, D. F. Walls, and M. J. Collett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.252 66, 252 (1991);
25. L. Hardy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.2279 73, 2279 (1994);
26. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.4571 74, 4571 (1995);
27. L. Vaidman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.2063 75, 2063 (1995);
28. D. M. Greenberger, M. A. Horne, and A. Zeilinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.2064 75, 2064 (1995);
29. L. Hardy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.2065 75, 2065 (1995).
30. H. M. Wiseman, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 6, S849 (2004).
31. For a detailed and amusing account, see S. D. Bartlett, T. Rudolph, and R. W. Spekkens, quant-ph/0507114.