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According to the continuum bipartite entangled state representation |η> we derive the Schmidt decomposition of |η>, respectively in the coordinate representation, momentum representation and the particle number representation, and explain their physical significances. As the applications of the Schmidt decomposition, we directly derive the action of the single-mode squeeze operator on |η>, the two-mode squeeze operator's entangled state representation, as well as the matrix element of displacement operator in the Fock space. Generalization of our discussion in this paper to the multipartite entangled state cases is feasible.
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Keywords:
- entangled state /
- Schmidt decomposition /
- squeezed operator
[1] Dirac P A M 1930 The Principles of Quantum Mechanics (Oxford:Clarendon Press)
[2] Glauber R 1963 J. Phys. Rev. 130 2529
[3] Glauber R 1963 J. Phys. Rev. 131 2766
[4] Reed M D, DiCarlo L, Nigg S E, Sun L, Frunzio L, Girvin S M, Schoelkopf R J 2012 Nature 482 382
[5] Li P B, Gao S Y, Li F L 2012 Phys. Rev. A 85 014303
[6] Cheng G L, Chen A X, Zhong W X 2011 Opt. Commun. 284 4028
[7] Hou S Y, Yang K 2011 Chin. Phys. Lett. 28 064203
[8] Hulya Y A, Alessio S 2011 Phys. Lett. A 375 1864
[9] Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 050303
[10] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 70
[11] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[12] Fan H Y, Fan Yue 1996 Phys. Rev. A 54 958
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[1] Dirac P A M 1930 The Principles of Quantum Mechanics (Oxford:Clarendon Press)
[2] Glauber R 1963 J. Phys. Rev. 130 2529
[3] Glauber R 1963 J. Phys. Rev. 131 2766
[4] Reed M D, DiCarlo L, Nigg S E, Sun L, Frunzio L, Girvin S M, Schoelkopf R J 2012 Nature 482 382
[5] Li P B, Gao S Y, Li F L 2012 Phys. Rev. A 85 014303
[6] Cheng G L, Chen A X, Zhong W X 2011 Opt. Commun. 284 4028
[7] Hou S Y, Yang K 2011 Chin. Phys. Lett. 28 064203
[8] Hulya Y A, Alessio S 2011 Phys. Lett. A 375 1864
[9] Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 050303
[10] Fan H Y, Klauder J R 1994 Phys. Rev. A 49 70
[11] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[12] Fan H Y, Fan Yue 1996 Phys. Rev. A 54 958
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