Electronic entanglement via quantum Hall interferometry in analogy to an optical method

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 20, 2009, Pages

  Frustaglia, Diego ^a   Cabello, Adán ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954738636     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.201312     Document Type: Article

References (32)

1. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337 (1995). 10.1103/PhysRevLett.75.4337
2. J. D. Franson, Phys. Rev. Lett. 62, 2205 (1989). 10.1103/PhysRevLett.62. 2205
3. Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, Nature (London) 422, 415 (2003). 10.1038/nature01503
4. M. Henny, S. Oberholzer, C. Strunk, T. Heinzel, K. Ensslin, M. Holland, and C. Schönenberger, Science 284, 296 (1999) 10.1126/science.284.5412.296
5. W. D. Oliver, J. Kim, R. C. Liu, and Y. Yamamoto, Science 284, 299 (1999) 10.1126/science.284.5412.299
6. S. Oberholzer, M. Henny, C. Strunk, C. Schönenberger, T. Heinzel, K. Ensslin, and M. Holland, Physica (Amsterdam) 6E, 314 (2000)
7. H. Kiesel, A. Renz, and F. Hasselbach, Nature (London) 418, 392 (2002). 10.1038/nature00911
8. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, and V. Umansky, Nature (London) 448, 333 (2007). 10.1038/nature05955
9. R. Hanbury Brown and R. Q. Twiss, Nature (London) 177, 27 (1956). 10.1038/177027a0
10. V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, Phys. Rev. B 74, 115315 (2006). 10.1103/PhysRevB.74.115315
11. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987). 10.1103/PhysRevLett.59.2044
12. A. Cabello, A. Rossi, G. Vallone, F. De Martini, and P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009). 10.1103/PhysRevLett.102.040401
13. C. W. J. Beenakker, C. Emary, M. Kindermann, and J. L. van Velsen, Phys. Rev. Lett. 91, 147901 (2003). 10.1103/PhysRevLett.91.147901
14. P. Samuelsson, E. V. Sukhorukov, and M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). 10.1103/PhysRevLett.92.026805
15. P. Samuelsson and M. Büttiker, Phys. Rev. B 71, 245317 (2005). 10.1103/PhysRevB.71.245317
16. H. M. Wiseman and J. A. Vaccaro, Phys. Rev. Lett. 91, 097902 (2003) 10.1103/PhysRevLett.91.097902
17. N. Schuch, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 92, 087904 (2004) 10.1103/PhysRevLett.92.087904
18. V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, Phys. Rev. B 75, 241305 (R) (2007). 10.1103/PhysRevB.75.241305
19. J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964)
20. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969). 10.1103/PhysRevLett.23.880
21. P. Samuelsson, E. V. Sukhorukov, and M. Büttiker, Phys. Rev. Lett. 91, 157002 (2003). 10.1103/PhysRevLett.91.157002
22. S. Aerts, P. G. Kwiat, J.-Å. Larsson, and M. Zukowski, Phys. Rev. Lett. 83, 2872 (1999) 10.1103/PhysRevLett.83.2872
23. S. Aerts, P. G. Kwiat, J.-Å. Larsson, and M. Zukowski, Phys. Rev. Lett. 86, 1909 (2001). 10.1103/PhysRevLett.86.1909
24. For the sake of simplicity, we consider the spinless case only. Spin-degenerate channels can be introduced without any significant consequence on orbital entanglement due to separability of spin and orbital degrees of freedom.
25. C. W. J. Beenakker, Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics "Enrico Fermi," Varenna, 2005 (IOS Press, Amsterdam, 2006).
26. P. Samuelsson, E. V. Sukhorukov, and M. Büttiker, N. J. Phys. 7, 176 (2005). 10.1088/1367-2630/7/1/176
27. We identify the two levels of each qubit with the pair of outgoing channels at each side of the interferometer (along which only one particle electron or hole propagates). Defining the upper state of each qubit as the electron excitation, |1« = C (L,R ) 1 † | 0̄ », and the lower state as the hole one, |0« = C (L,R ) 2 | 0̄ », the first two terms in Eq. read as t1 t2*- | 10 « - r1 r2*| 01 ».
28. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998). 10.1103/PhysRevLett.80. 2245
29. M. Büttiker, Phys. Rev. Lett. 65, 2901 (1990). 10.1103/PhysRevLett. 65.2901
30. The U L and U R mixing matrices can absorb the kinetic/magnetic phases acquired by the electrons (and holes) along their way from BS-1 and BS-2 to drains, so we do not need to consider them explicitly. Notice that the mixing can be performed either by controlling the transmission amplitude of BS-L and BS-R by modifying the Aharonov-Bohm flux through the interferometer or by introducing local electric gates that modify the length of selected paths toward the left and/or right side of the interferometer.
31. S. Popescu and D. Rohrlich, Phys. Lett. A 166, 293 (1992). 10.1016/0375-9601(92)90711-T
32. N. Gisin, Phys. Lett. A 154, 201 (1991). 10.1016/0375-9601(91)90805-I