LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Reid, M. D. (2001)
Languages: English
Types: Preprint
Subjects:

Classified by OpenAIRE into

arxiv: Quantum Physics, Physics::History of Physics
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of (Bell-type) local realistic theories which could be consistent with a local quantum description for each subsystem. The relationship with criteria sufficient to prove entanglement is established, to show that any demonstration of EPR correlations will also signify entanglement. It is also shown how a demonstration of entanglement between two spatially separated subsystems, if not able to interpreted as a violation of a Bell-type inequality, may be interpreted as a demonstration of the EPR correlations. In particular it is explained how the experimental observation of two-mode squeezing using spatially separated detectors will signify not only entanglement but EPR correlations defined in a general sense.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47, 777, (1935).
    • [2] J. S. Bell, Physics, 1, 195, (1965). J. S. Bell, “Speakable and Unspeakable in Quantum Mechanics” (Cambridge Univ. Press, Cambridge, 1988).
    • [3] J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).
    • [4] M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731, (1988). P. Grangier, M. J. Potasek and B. Yurke, Phys. Rev. A 38, 3132, (1988). B. J. Oliver and C. R. Stroud, Phys. Lett. A 135, 407, (1989).
    • [5] M. D. Reid, Phys. Rev. A 40, 913 (1989).
    • [6] C. M. Caves and B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker, Phys. Rev. A 31, 3093 (1985).
    • [7] M. D. Reid and P.D. Drummond, Phys. Rev. A40, 4493 (1989). P. D. Drummond and M. D. Reid, Phys. Rev. A41, 3930 (1990).
    • [8] Z. Y. Ou, S. F. Pereira, H. J. Kimble and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
    • [9] Yun Zhang, Hai Wang, Xiaoying Li,Jietai Jing, Changde Xie and Kunchi Peng, Phys. Rev. A 62, 023813 (2000).
    • [10] Ch. Silberhorn, P. K. Lam, O. Weiss, F. Koenig, N. Korolkova and G. Leuchs, Phys. Rev. Lett. 86, 4267 (20001).
    • [11] K. Tara and G. S. Agarwal, Phys. Rev. A 50, 2870, (1994).
    • [12] V. Giovannetti, S. Mancini and P. Tombesi, quantph/0005066.
    • [13] A. Furasawa, J. Sorensen, S. Braunstein, C. Fuchs, H. Kimble and E. Polzik, Science 282, 706 (1998); L. Vaidmann, Phys. Rev. A 49, 1473 (1994); S. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869 (1998); A. Kuzmich and E. S. Polzik, Phys. Rev. Lett. 85, 5639 (2000); I. V. Sokolov, M. I. Kolobov, A. Gatti, L. A. Lugiato, quant-ph/0007026.
    • [14] T. C. Ralph, Phys. Rev. A 61, 303 (1999); Phys. Rev. A 62 062306 (2000). M. Hillery, Phys. Rev. A 61, 2309 (1999). M. D. Reid, Phys. Rev. A62, 062308 (2000). N. J. Cerf, M. Levy and G. Van Assche, Phys. Rev. A 63 052311 (2001). S. F. Pereira, Z. Y. Ou and H. J. Kimble, quant-ph/0003094. P. Navez, A. Gatti and G. Lugiato, quant-ph/0101113; ibid, to be published. Ch. Silberhorn et al, Europe IQEC (2000). See also L. M. Duan, J. I. Cirac, P. Zoller, Phys. Rev. Lett. 85, 5643 (2000).
    • [15] A. Aspect, P. Grangier and G. Roger, Phys. Rev. Lett. 49, 91, (1982). A. Zeilinger, Rev. Mod. Phys. 71, 5288, (1998).
    • [16] E. Schr¨odinger, Naturwissenschaften 23, 807 (1935).
    • [17] M.A. Rowe, D. Kielpinski,V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, D. J. Wineland, Nature 409, 791 (2001).
    • [18] M. D. Reid, Europhys. Lett. 36, 1 (1996); quantph/0101050. M. D. Reid, Phys. Rev. Lett, 84, 2765 (2000); Phys. Rev. A. 62, 022110 (2000).
    • [19] P. D. Drummond, Phys. Rev. Lett. 50, 1407 (1983). N. D. Mermin, Phys. Rev. D 22, 356 (1980); M. D. Reid, W. J. Munro and F. De Martini, quant-ph/0104139; A. Lamas-Linares, JC. Howell and D. Bouwmeester, Nature 412,6850 (20001).
    • [20] L. Duan, G. Giedke, J. I. Cirac and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000); R. Simon, Phys. Rev. Lett. 84, 2726 (2000). See also P. Horodecki and M. Lewenstein, Phys. Rev. Lett. 85 2657, (2000). R. F. Werner and M. M. Wolf, quant-ph/0009118.
    • [21] M. D. Reid, quant-ph/0103142.
    • [22] A. K. Ekert, Phys. Rev. Lett, 67, 661 (1991). A. K. Ekert, B. Huttner, G. M. Palma and A. Peres, Phys. Rev. A 50, 1047 (1994).
    • [23] M. D. Reid, quant-ph/0112039.
    • [24] This choice d = μi will minimize the rms error ph(x|xiB − d)2i where x|xiB refers to results x at A, conditional on a result xiB at B.
    • [25] The proven failure of one of the more general EPR criteria (based on (19) and (20)) will not necessarily imply that the 1989 EPR inferred H. U. P. criterion (12) has been met. How this difference comes about may be understood by the following example. This stronger 1989 EPR criterion requires certain restrictions on the average of the variances of the conditional distributions. Consider a system with the following local hidden variable description: suppose the system is in a hidden variable state {1, 1, 1, 2} with probability P1; or in an alternative state {3, 2, 1, 4} with probability P2, where the values of the hidden variables give the precise results of measurements xˆ, pˆ, xˆB, pˆB respectively if measured. In this case then the predicted results for measurement given a particular hidden variable state are definite: Δλ = 0. The result 1 for measurement xˆB at B is correlated with both 1 and 3 for measurement xˆ at A. The measured variance in the conditional distribution P (x|xiB = 1), the probability of result x for xˆ given result xiB = 1 for xˆB, can be substantial despite the definiteness of the local hidden variable description. The failure to demonstrate a direct EPR situation through conditional measurements does not however mean that the statistics can be explained through an entirely local realistic description (as given practically by (19)) where local subsystems could be represented by quantum states.
    • [26] It is certainly true however that for the case of perfect EPR correlations where all Δix, Δj p = 0, it is required of any local realistic theory that all Δλx = Δλp = 0 to give hidden variables with definite predictions for xˆ and pˆ. This is proved explicitly in the Appendix (as is the case of near-perfect correlation), and gives the situation of the original EPR paradox discussed in Section 3a.
    • [27] The degree of fuzziness however cannot be determined directly from the values Δi2x, Δj p for the variances of 2 the conditional distributions. This is because poor correlation between results for A and B can be described, in a way perfectly consistent with local realism, using local realistic (hidden) variables with varying definiteness Δλx Δλp, depending on the degree of correlation between the underlying local realistic variables describing the subsystems A and B. For example we may have poorlycorrelated variables with definite predictions (Δλx, Δλp are zero), or well-correlated variables for A and B which have with fuzzy predictions (Δλx, Δλp are large).
    • [28] A. Peres, Phys. Rev. Lett. 77, 1413,(1996); M. Horodecki et al, Phys. Lett. A 223,1 (1996).
    • [29] S. L. Braunstein et al, quant-ph/0012001
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article

Collected from