Abstract
We propose an entangled fractional squeezing transformation (EFrST) generated by using two mutually conjugate entangled state representations with the following operator: \(e^{ - i\alpha \left( {a_1^\dag a_2^\dag + a_1 a_2 } \right)} e^{i\pi a_2^\dag a_2 }\); this transformation sharply contrasts the complex fractional Fourier transformation produced by using \(e^{ - i\alpha \left( {a_1^\dag a_1 + a_2^\dag a_2 } \right)} e^{i\pi a_2^\dag a_2 }\) (see Front. Phys. DOI: 10.1007/s11467-014-0445-x). The EFrST is obtained by converting the triangular functions in the integration kernel of the usual fractional Fourier transformation into hyperbolic functions, i.e., tanα → tanhα and sinα → sinh α. The fractional property of the EFrST can be well described by virtue of the properties of the entangled state representations.
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Fan, HY., Chen, JH. & Zhang, PF. On the entangled fractional squeezing transformation. Front. Phys. 10, 187–191 (2015). https://doi.org/10.1007/s11467-014-0457-6
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DOI: https://doi.org/10.1007/s11467-014-0457-6