New fractional entangling transform and its quantum mechanical correspondence

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 mechanic