Abstract
The known Peres-Horodecki criterion and scaling criterion of separability are considered on examples of three-mode and four-mode Gaussian states of electromagnetic field. It is shown that the principal minors of the photon-quadrature dispersion matrix are sensitive to the change of scaling parameters. An empirical observation has shown that the bigger the modulus of negative principal minors, the more entangled the state.
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R. Simon, Phys. Rev. Lett., 84, 2726 (2000).
L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett., 84, 2722 (2000).
A. Peres, Phys. Rev. Lett., 77, 1413 (1996).
P. Horodecki, R. Horodecki, and M. Horodecki, Phys. Lett. A, 223, 1 (1996).
E. C. G. Sudarshan, R. J. Mathews, and J. Rau, Phys. Rev., 121, 920 (1961).
E. Shchukin and W. Vogel, Phys. Rev. Lett., 95, 230502 (2005).
E. Shchukin and W. Vogel, Phys. Rev. Lett., 96, 200403 (2006).
E. Shchukin and W. Vogel, Phys. Rev. A, 74, 030302 (2006).
G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A, 73, 032345 (2006).
O. V. Man’ko, V. I. Man’ko, G. Marmo, et al., Phys. Lett. A, 339, 194 (2005).
O. V. Man’ko, V. I. Man’ko, G. Marmo, et al., Phys. Lett. A, 357, 255 (2006).
E. Wigner, Phys. Rev., 40, 749 (1932).
A. S. Chirkin and M. Yu. Saigin, Acta Phys. Hung. B, 26/1–2, 63 (2006).
M. Yu. Saigin and A. S. Chirkin, Mod. Probl. Stat. Phys., 5, 169 (2006).
E. Schrodinger, Ber. Kgl. Akad. Wiss. Berlin, 24, 296 (1930).
H. P. Robertson, Phys. Rev., 35, 667 (1930).
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Manuscript submitted by the authors in English on August 30, 2007.
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Man’ko, V.I., Sergeevich, A.A. Separability and entanglement of four-mode Gaussian states. J Russ Laser Res 28, 516–528 (2007). https://doi.org/10.1007/s10946-007-0039-y
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DOI: https://doi.org/10.1007/s10946-007-0039-y