Solution to Operator Fredholm Equation in Bipartite Entangled State Representation and Its Applications

Wen-Jian Yu, Hong‐Chun Yuan, Ji‐Suo Wang

Meng Yang, Ji‐Suo Wang, Xiang‐Guo Meng

Fan Hong‐Yi, Ji‐Suo Wang

Based on the bipartite entangled state representation and using the technique of integration within an ordered product (IWOP) of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and new relations about the two-variable Hermite polynomials.

Hong-Yi Fan, Qin Guo

Based on the intermediate coordinate-momentum representations, we construct the appropriate generalized Fredholm operator equation and then find its solution. The application of this equation for deriving Hermite-polynomial operator formulae is demonstrated. The connection of the generalized Wigner operator to the form of the Gaussian bivariate distribution of random variables in statistics is shown, which is useful for studying the tomogram of quantum states.

Roman Gielerak, Joanna Wiśniewska, Marek Sawerwain

Hong-Yi Fan, John R. Klauder

Using the technique of integration within an ordered product of operators we construct operator Fredholm equations, which can help us to re-formulize the Weyl correspondence and P-representation. We then search for their solutions which present new formulae for deriving quantum operators' Weyl classical correspondence and P-representation. As the application, we deduce some new relations about the two-variable Hermite polynomials.