Abstract

The purpose of this paper is to deduce an analytical expression for the violation of Bell's inequality by quantum theory and plane trigonometry, and expound the violation and maximal violation of the first, second type Bell's inequality in detail. Further, we find out the sufficient conditions for the region in which Bell's inequalities are violated.

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  1. J. S. Bell, Physics 1, 195 (1964).
  2. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
  3. B. S. Cirel'son, Lett. Math. Phys. 4, 93 (1980).
  4. L. J. Landau, Phys. Lett. A 120, 54 (1987).
  5. N. Gisin and A. Peres, Phys. Lett. A 162, 15 (1992).
  6. N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).
  7. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
  8. J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).
  9. J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).
  10. S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972).
  11. Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
  12. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
  13. N. Bohr, Phys. Rev. 48, 696 (1935).
  14. D. Bohm, Quantum Theory (2nd ed.) (Englewood Cliffs, NJ, 1951) p. 614.

1992 (1)

N. Gisin and A. Peres, Phys. Lett. A 162, 15 (1992).

1990 (2)

N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

1988 (1)

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).

1987 (1)

L. J. Landau, Phys. Lett. A 120, 54 (1987).

1980 (1)

B. S. Cirel'son, Lett. Math. Phys. 4, 93 (1980).

1978 (1)

J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).

1974 (1)

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).

1972 (1)

S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972).

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

1964 (1)

J. S. Bell, Physics 1, 195 (1964).

1935 (2)

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

N. Bohr, Phys. Rev. 48, 696 (1935).

Alley, C. O.

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).

Bell, J. S.

J. S. Bell, Physics 1, 195 (1964).

Bohr, N.

N. Bohr, Phys. Rev. 48, 696 (1935).

Cirel'son, B. S.

B. S. Cirel'son, Lett. Math. Phys. 4, 93 (1980).

Clauser, J. F.

J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).

S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972).

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

Freedman, S. J.

S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972).

Gisin, N.

N. Gisin and A. Peres, Phys. Lett. A 162, 15 (1992).

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

Horne, M. A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

Landau, L. J.

L. J. Landau, Phys. Lett. A 120, 54 (1987).

Mermin, N. D.

N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).

Peres, A.

N. Gisin and A. Peres, Phys. Lett. A 162, 15 (1992).

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

Shih, Y. H.

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).

Shimony, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

Zeilinger, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Am. J. Phys. (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Lett. Math. Phys. (1)

B. S. Cirel'son, Lett. Math. Phys. 4, 93 (1980).

Phys. Lett. A (2)

L. J. Landau, Phys. Lett. A 120, 54 (1987).

N. Gisin and A. Peres, Phys. Lett. A 162, 15 (1992).

Phys. Rev. (2)

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

N. Bohr, Phys. Rev. 48, 696 (1935).

Phys. Rev. D (1)

J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974).

Phys. Rev. Lett. (4)

S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972).

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).

N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

Physics (1)

J. S. Bell, Physics 1, 195 (1964).

Rep. Prog. Phys. (1)

J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).

Other (1)

D. Bohm, Quantum Theory (2nd ed.) (Englewood Cliffs, NJ, 1951) p. 614.

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