Measurement-induced decoherence in a simple quantum system

Measurement-induced decoherence and its consequent effect on the time evolution of the measured system is investigated via the Wigner representation W. Using a discrete-state computer model put forward by Wallace [D. Wallace, Phys. Rev. A 63, 022109 (2001)], we simulate a free particle moving in a periodic space, which is subjected to repeated projection-valued measurements of position. The measurements are made at rapid intervals, such as to induce a Zeno effect in the motion of the particle. We construct a discrete form of the Wigner distribution, which is used to represent the system ensemble at various times during its evolution. In addition, we calculate the entropy of the system ensemble and compare its time development with the Wigner distribution of the system state. We conclude that, in accordance with the findings of other similar investigations, the attenuation of negative W is a measure of the increasing decoherence in the system density operator, and is characteristic of the transition from the quantum to the classical descriptions of the system.