Phase Space Analysis of the Two-mode Binomial State Produced by Quantum Entanglement in a Beamsplitter

摘要

Phase space analysis of quantum states is a newly developed topic in quantum optics. In this work we present Wigner phase space distributions for the two-mode binomial state produced by quantum entanglement between a vacuum state and a number state in a beamsplitter. By using two new binomial formulas involving two-variable Hermite polynomials and the so-called entangled Wigner operator, we find that the analytical Wigner function for the binomial state |xi >(q) equivalent to D(xi) |q, 0 > is related to a Laguerre polynomial, i.e.,