2006
Journal article
Open Access
Tomographic test of Bells inequality for a time-delocalized single photon
D'Angelo M., Zavatta A., Parigi V., Bellini M.
Atomic and Molecular Physics quantum optics and Optics Quantum Physics (quant-ph) Quantum Physics FOS: Physical sciences
Time-domain balanced homodyne detection is performed on two well-separated temporal modes sharing a single photon. The reconstructed density matrix of the two-mode system is used to prove and quantify its entangled nature, while theWigner function is employed for an innovative tomographic test of Bells inequality based on the theoretical proposal by Banaszek and Wodkiewicz (Phys. Rev. Lett. 82, pp.2009 1999). Provided some auxiliary assumptions are made, a clear violation of the Banaszek-Bell inequality is found.
Source: Physical review. A 74 (2006): 052114–052114. doi:10.1103/PhysRevA.74.052114
Publisher: Published by the American Physical Society through the American Institute of Physics,, New York, N.Y. , Stati Uniti d'America
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[25] G. Vidal and R. F. Werner, Phys. Rev. A 65, 032314 (2002)
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[28] A. Zavatta, et al., Phys. Rev. A 70, 053821 (2004)
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[32] By defining the purity parameter as P = T r(ρˆs2), we get, in the spectral and the spatial domains, respectively: Pspectral = 1/p1 + Δωi2/Δωp2 = .98, and Pspatial = 2 2 1/(1 + Δκi /Δκp) = .86, where Gaussian profiles with spectral and spatial widths Δωj2 and Δκj2 are assumed both for the pump power spectrum (j = p) and for the filter transmission function in the idler channel (j = i). The contribution of purity to the single-photon preparation efficiency is: ηpurity = pPspectralPspatial = .92.
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[35] K. Banaszek, et al., Phys. Rev. A 61, 010304(R) (1999)
[36] T. Kiss, et al., Phys. Rev. A 52, 2433 (1995)
[37] After the vacuum-cleaning procedure, we find EN (ρˆ) = 0.99 ± 0.01, which is very close to the unitary value expected for the pure state of Eq. (2). The amount of entanglement required for observing a violation of BanaszekBell's inequality is EN > 0.942; as far as the identification of entanglement is concerned, the more restrictive bounds imposed by Bell's inequality with respect to Peres criterion appear here explicitly.
[38] In this respect, it is worth reminding that also the first by A. Aspect et al. (PRL 49, 1804 (1982)).
[2] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)
[3] J.S. Bell, Physics 1, 195 (1964)
[4] D. Bohm, Quantum Theory, Prentice-Hall, Englewood Cliffs, NJ, 1951
[5] The most common auxiliary assumptions involved in the experimental tests of Bell's inequality are: 1) the fairsampling assumption, namely, the hypothesis that undetected events coming from low detection efficiencies would follow the same statistics of the measured data set, 2) post-selection, which consists in disregarding part of the state of a physical system by not measuring it (i.e., imposing a selective, or state-dependent, loss mechanism) 3) the locality-loophole, which arises whenever a physical signal could be exchanged between the two systems under investigation during the measurement process.
[6] C.H. Bennett, et al., Nature 404, 247 (2000)
[7] S.M. Tan, D.F. Walls, and M.J. Collett, Phys. Rev. Lett. 66, 252 (1991)
[8] E. Santos, Phys. Rev. Lett. 68, 894 (1992); L. Hardy, ibid. 75, 2065 (1995) and refs. therein; D.M. Greenberger, et al. ibid. 75, 2064 (1995); A. Peres, ibid. 74, 4571 (1995); D. Horne, et al., Phys. Lett. A 209, 1 (1995); K. Jacobs, et al., Phys. Rev. A 54, R3738 (1996)
[9] L. Hardy, Phys. Rev. Lett. 73, 2279 (1994)
[10] K. Banaszek, and K. Wodkiewicz, Phys. Rev. A 58, 4345 (1998); Phys. Rev. Lett. 82, 2009 (1999)
[11] S.A. Babichev, et al., Phys. Rev. Lett. 92, 193601 (2004)
[12] B. Hessmo, et. al. Phys. Rev. Lett. 92, 180401 (2004)
[13] S. J. Van Enk, Phys. Rev. A 72, 064306 (2005)
[14] A. Zavatta, et al., Phys. Rev. Lett. 96, 020502 (2006)
[15] M. Pawlowski and M. Czachor, quant-ph/0507151, and Phys. Rev. A 73, 042111 (2006)
[16] U. Leonhardt, Measuring the Quantum State of Light, Cambridge University Press, Cambridge, 1997
[17] M.G.A. Paris and J. Rehacek (Eds.), Quantum State Estimation (Springer, Berlin, 2004).
[18] S. Giacomini et al., Phys. Rev. A 66, 030302 (2002)
[19] H. de Riedmatten et al., Phys. Rev. Lett. 92, 047904 (2004)
[20] E. Knill, et al., Nature (London) 409, 46 (2001)
[21] T. B. Pittman, et al., Phys. Rev. A 71, 032307 (2005)
[22] J. Brendel, et al., Phys. Rev. Lett. 82, 2594 (1999); H. de Riedmatten, et al., Phys. Rev. A 69, 050304 (2004)
[23] C. Simon, et al., Phys. Rev. Lett. 94, 030502 (2005)
[24] I. Marcikic, et al., Nature (London) 421, 509 (2003)
[25] G. Vidal and R. F. Werner, Phys. Rev. A 65, 032314 (2002)
[26] A. Peres, Phys. Rev. Lett. 77, 1413 (1996)
[27] B. Yurke, et al., Phys. Rev. Lett. 79, 4941 (1997); J. Wenger, et al., Phys. Rev. A 67, 012105 (2003); S. Daffer, et al., ibid 72, 034101 (2005)
[28] A. Zavatta, et al., Phys. Rev. A 70, 053821 (2004)
[29] A. Zavatta, et al., Science 306, 660 (2004), and Phys. Rev. A 72, 023820 (2005)
[30] T.E. Keller, and M.H. Rubin, Phys. Rev. A 56, 1534 (1997); Y.-H. Kim, et al., Phys. Rev. A 62, 043820 (2000)
[31] A.I. Lvovsky, et al., Phys. Rev. Lett. 87, 050402 (2001)
[32] By defining the purity parameter as P = T r(ρˆs2), we get, in the spectral and the spatial domains, respectively: Pspectral = 1/p1 + Δωi2/Δωp2 = .98, and Pspatial = 2 2 1/(1 + Δκi /Δκp) = .86, where Gaussian profiles with spectral and spatial widths Δωj2 and Δκj2 are assumed both for the pump power spectrum (j = p) and for the filter transmission function in the idler channel (j = i). The contribution of purity to the single-photon preparation efficiency is: ηpurity = pPspectralPspatial = .92.
[33] G. M. D'Ariano, et al., Phys. Rev. A 50, 4298 (1994).
[34] G. M. D'Ariano in Quantum optics and Spectroscopy of Solids, edited by T. Hakioglu and A. Shumovsky (Kluwer Academic, Dordrecht, 1997), pp. 175-202.
[35] K. Banaszek, et al., Phys. Rev. A 61, 010304(R) (1999)
[36] T. Kiss, et al., Phys. Rev. A 52, 2433 (1995)
[37] After the vacuum-cleaning procedure, we find EN (ρˆ) = 0.99 ± 0.01, which is very close to the unitary value expected for the pure state of Eq. (2). The amount of entanglement required for observing a violation of BanaszekBell's inequality is EN > 0.942; as far as the identification of entanglement is concerned, the more restrictive bounds imposed by Bell's inequality with respect to Peres criterion appear here explicitly.
[38] In this respect, it is worth reminding that also the first by A. Aspect et al. (PRL 49, 1804 (1982)).
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BibTeX entry
@article{oai:it.cnr:prodotti:57856,
title = {Tomographic test of Bells inequality for a time-delocalized single photon},
author = {D'Angelo M. and Zavatta A. and Parigi V. and Bellini M.},
publisher = {Published by the American Physical Society through the American Institute of Physics,, New York, N.Y. , Stati Uniti d'America},
doi = {10.1103/physreva.74.052114 and 10.48550/arxiv.quant-ph/0602150},
journal = {Physical review. A},
volume = {74},
pages = {052114–052114},
year = {2006}
}
