Jeffrey Schenker
Michigan State University
Title
Quantum Trajectories under Repeated Generalized Measurements
Abstract
In his classic text, von Neumann emphasized that quantum mechanics contains “two fundamentally different types” of state changes: unitary evolution and measurement. Although Born's rule provides an unambiguous procedure for computing the probability distribution for the outcomes of a measurement, the state change induced by a measurement, sometimes referred to as “the collapse of the wave function,” is less clearly defined. In the 1960's and 1970's, careful physical analyses led to the formulation of the notion of "generalized" measurement, in which an ancillary system is measured and then discarded.
In this talk, a general framework for describing "quantum trajectories," i.e., the evolution of the state of a system under repeated generalized measurements, will be described. At a mathematical level, quantum trajectories are a particular type of Markov chains. Two classes of results will be discussed: 1) results on asymptotic purification of quantum trajectories, originally due to Kümmerer and Maassen, and 2) more recent work by various authors on large deviation principles for the results of measurements. In each case, recent work of the PI and coauthors has generalized these results to repeated random measurements subject to stationary and ergodic noise.