Abstract
Using a non-Gaussian operation—photon subtraction from two-mode squeezed thermal state (PS-TMSTS), we construct a kind of entangled state. A Jacobi polynomial is found to be related to the normalization factor. The negativity of Wigner function (WF) is used to discuss its nonclassicality. The investigated entanglement properties turn out that the symmetrical PS-TMSTS may be more effective than the non-symmetric for quantum teleportation. Then the time evolution of WF is used to examine the decoherence effect, which indicates that the characteristic time of single PS-TMSTS depends not only on the average photon number of environment, but also on the average photon number of thermal state and the squeezing parameter.
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Acknowledgements
This project was supported by the National Natural Science Foundation of China (Grant no. 11264018), and the Natural Science Foundation of Jiangxi Province of China (No. 20132BAB212006) as well as the Sponsored Program for Cultivating Youths of Outstanding Ability in Jiangxi Normal University.
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Appendices
Appendix A: Derivation of Eq. (16)
Substituting Eq. (15) into Eq. (14) and using Eq. (11), we have
where W 0(α,β) is defined in Eq. (17), and
and
as well as
Expanding the partial exponential items in Eq. (A2), then Eq. (A2) becomes
Further using the generating function of two-variable Hermite polynomials,
Equation (A5) can be put into the following form
Using the relation
thus we can obtain Eq. (18).
Appendix B: Derivation of Eq. (27)
Using the displacement operator \(D_{a} ( \alpha ) =e^{-\vert \alpha \vert ^{2}/2}e^{\alpha a^{\dagger}}e^{-\alpha^{\ast}a}\) and \(D_{b} ( \beta ) =e^{-\vert \beta \vert ^{2}/2}e^{\beta b^{\dagger}}e^{-\beta^{\ast}b}\), the CF of PS-TMSTS is given by
In a similar way to derive Eq. (10), using (10), one can directly obtain
Taking the following transformations
which leads to
thus Eq. (B2) becomes Eq. (27).
Appendix C: Derivation of Eq. (37)
Substituting Eq. (16) into Eq. (36), we have
where (g 0,g 1,g 2,g 3) and (μ 1,μ 2,G,Δ1) are defined in Eqs. (39) and (40), respectively. In a similar way to deriving Eq. (18), we can further insert Eq. (C1) into Eqs. (37)–(38).
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Zhang, HL., Hu, YQ., Jia, F. et al. Entanglement of Photon-Subtracted Two-Mode Squeezed Thermal State and Its Decoherence in Thermal Environments. Int J Theor Phys 53, 2091–2107 (2014). https://doi.org/10.1007/s10773-014-2015-y
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DOI: https://doi.org/10.1007/s10773-014-2015-y