我们发现量子光学理论中一个新的积分变换,它不但能够反映量子光学中的Baker-Hausdorff公式的功效,而且可以实现相空间多项式和纠缠态的函数空间之间的变换。此变换可逆,且满足类Parseval定理。在相空间中结合Wigner变换和此新积分变换,可以得到相空间函数h(p,q)和其Weyl-Wigner对应算符之间的一个新的积分变换公式。

We find a new kind of integration transformation in quantum optics, which can reflect the Baker-Hausdorff formula as well as establish the transformation between phase space basis and the function space of entangled state. This transformation is invertible and satisfies Parseval-like theorem. Combining Wigner transformation and this new transformation in phase space, We can acquire a new relation between phase space function h(p,q) and corresponding Weyl-Wigner operator, which can benefit the development of quantum phase space theory.