Quantum Dynamics in Wigner Phase Space

Abstract

Classical systems have a definite position and momentum, which can be visualised using a point in the phase space. Analogous treatment to classical phase space in quantum mechanics gives rise to quasi-probability distributions. One such representation is the Wigner function, which is very helpful to visualise quant m states at different points. We define and visualise the discrete Wigner function for various quantum states and their evolution. We perform experiments for the tomography of the Wigner function and find how the Wigner function can be used to find unknown quantum states. We find a computationally inexpensive method to distinguish between amplitude damping, dephasing and depolarisation channel in Wigner phase space. We also examine phase transitions from the perspective and how they connect to the Wigner phase space formalism. We also look at quantum chaos and the classical-quantum correspondence using the quantum kicked-top model.