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Problems generate, create code128b none with .net projects Beaware of Malicious QR Codes 1. In the perturba .net framework Code128 tion expansion of Eq.

(9.8), in rst order the output of a type I downconverter is the pair state . 1 s . 1 i . (a) Show that, in the second order, the output is the pair state 2 s . 2 i . (b) Supposin .net vs 2010 Code 128 g that the two photons within each of the states, and both pairs of the photons, simultaneously fall onto the inputs of a 50:50 beam splitter, what will be the output state (c) Show that your result does not agree with that which would be obtained classically using a simple binomial distribution.

(d) Devise an experiment able to discriminate between the quantum mechanical and classical predictions for the oputput of the beam splitter. (After working through this problem you may wish to consult a paper by Ou, Rhee and Wang [35].) 2.

Derive a CHSH Bell inequality starting from the Bell state . 1 = (. H 1 . V 2 . + . V 1 . H 2 ).. 3. As mentioned in the text above and in References [23] and [24], by using back-to-back type I down-converters, where one is rotated by 90 around the normal to the other and where both are pumped by light polarized at 45 , the Bell state . 1 = (. H 1 . H 2 . + . V 1 . V 2 ). Optical test of quantum mechanics can be produced. A nalyse the possible violations of Bell s inequalities (in the form of CHSH) with respect to this state. 4.

For the state . , consider the quantity SBell C( , ) C( , ). + . C( , ) + C( , ). . Show, for a loca code-128c for .NET l realistic theory, where we replace C( , ) by CHV ( , ), that SBell 2.

Find an example where quantum mechanics violates the inequality. (This is the inequality originally discussed by Bell.).

References [1] J. S. Bell, Ph barcode 128 for .

NET ysics (NY), 1 (1964), 195. See also J. S.

Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press, 1987). [2] D. Bohm, Phys.

Rev. 85 (1952), 166, 180. [3] D.

C. Burnham and D. L.

Weinberg, Phys. Rev. Lett.

, 25 (1970), 84. [4] A. Joobeur, B.

Saleh and M. Teich, Phys. Rev.

A, 50 (1994), 3349. [5] See, for example, R. W.

Boyd, Nonlinear Optics, 2nd edition (San Diego: Academic Press, 2003). [6] C. K.

Hong, Z. Y. Ou and L.

Mandel, Phys. Rev. Lett.

, 59 (1987), 2044. A related experiment was later performed by J. G.

Rarity, P. R. Tapster, E.

Jakeman, T. Larchuk, R. A.

Campos, M. C. Teich and B.

E. A. Saleh, Phys.

Rev. Lett., 65 (1990), 1348.

[7] P. G. Kwiat, A.

M. Steinberg and R. Y.

Chiao, Phys. Rev. A, 45 (1992), 7729.

[8] D. M. Greenberger, M.

A. Horne and A. Zeilinger, Physics Today (August 1993), p.

22. [9] X. Y.

Zou, L. J. Wang and L.

Mandel, Phys. Rev. Lett.

, 67 (1991), 318. [10] R. Y.

Chiao and A. M. Steinberg, Progress in Optics XXXVII, E.

Wolf (editor) (Amsterdam: Elsevier, 1997), p. 345; G. Nimtz and W.

Heitmann, Prog. Quant. Electr.

, 21 (1997), 81. [11] A. M.

Steinberg, P. G. Kwiat and R.

Y. Chiao, Phys. Rev.

Lett., 71 (1993), 708. [12] See H.

Winful, Phys. Rev. Lett.

, 90 (2003), 023901; M. B ttiker and S. Washburn, u Nature, 422 (2003), 271; and the exchange between Winful and B ttiker and Washburn, u Nature 424 (2003), 638.

[13] See any good optics text such as F. L. Pedrotti and L.

S. Pedrotti, Introduction to Optics, 2nd edition (Englewood Cliffs: Prentice Hall, 1993). For a discussion of polarized single-photon states and the use of calcite crystals to detect them, along with a discussion of their use in elucidating a number of puzzling features in quantum mechanics, see A.

P. French and E. F.

Taylor, An Introduction to Quantum Physics (New York: W. W. Norton, 1978), chapter 6.

[14] See W. Tittel and G. Weihs, Quant.

Inf. Comp., 1 (2001), 3; Y.

Shih, Rep. Prog. Phys.

, 66 (2003), 1009. [15] A. Einstein, B.

Podolsky and N. Rosen, Phys. Rev.

, 47 (1935), 777. [16] D. Bohm, Quantum Theory (New York: Prentice-Hall, 1951), chapter 22.

[17] J. F. Clauser, M.

A. Horne, A. Shimony and R.

A. Holt, Phys. Rev.

Lett., 23 (1969), 880. [18] S.

J. Freedman and J. F.

Clauser, Phys. Rev. Lett.

, 28 (1972), 938. [19] A. Aspect, P.

Grangier and G. Roger, Phys. Rev.

Lett., 49 (1982), 91. [20] A.

Aspect, J. Dalibard and G. Roger, Phys.

Rev. Lett., 49 (1982), 1804.

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