摘要
In this Letter, a new fractional entangling transformation （FRET） is proposed, which is generated in the entangled state representation by a unitary operator exp{iθ（ab^＋ ＋ a^＋ b）} where a（b） is the Bosonic annihilate operator. The operator is actually an entangled one in quantum optics and differs evidently from the separable operator, exp（iθ（a^＋a＋ b^＋ b）}, of complex fractional Fourier transformation. The additivity property is proved by employing the entangled state representation and quantum mechanical version of the FRET. As an application, the FrET of a two-mode number state is derived directly by using the quantum version of the FRET, which is related to Hermite polynomials.
In this Letter, a new fractional entangling transformation （FRET） is proposed, which is generated in the entangled state representation by a unitary operator exp{iθ（ab^＋ ＋ a^＋ b）} where a（b） is the Bosonic annihilate operator. The operator is actually an entangled one in quantum optics and differs evidently from the separable operator, exp（iθ（a^＋a＋ b^＋ b）}, of complex fractional Fourier transformation. The additivity property is proved by employing the entangled state representation and quantum mechanical version of the FRET. As an application, the FrET of a two-mode number state is derived directly by using the quantum version of the FRET, which is related to Hermite polynomials.
基金
supported by the National Natural Science Foundation of China(Grant Nos.11264018 and11174118)
the Natural Science Foundation of Jiangxi Province of China(Grant No.20132BAB212006)
the Research Foundation of the Education Department of Jiangxi Province of China(No.GJJ14274)
the Degree and Postgraduate Education Teaching Reform Project of Jiangxi Province(No.JXYJG-2013-027)
