William Wootters, Williams College, Williamstown, USA
For a particle moving in one dimension, phase space is a two-dimensional real vector space whose axes are associated with
position and momentum. In this talk I present a generalization of phase space for discrete quantum systems, in which the analogs of position and momentum take values in a finite field. In this framework, a quantum state is represented by its Wigner function, a real function on the discrete phase space that behaves in some respects like a probability distribution but can take negative
values. The phase space representation is closely related to certain symmetric measurements useful for "quantum tomography." It also provides a way of generating special sets of quantum states that have natural classical interpretations.
