Exact Pointer Properties for Quantum System Projector Measurements with Application to Weak Measurements and Their Accuracy

摘要

Exact pointer states are obtained for projection operator measurementsperformed upon pre-selected (PS) and upon pre- and post-selected (PPS) quantumsystems. These states are used to provide simple exact expressions for both thepointer spatial probability distribution profiles and the mean values ofarbitrary pointer observables associated with PS and PPS projection operatormeasurements that are valid for any strength of the interaction which couples ameasurement pointer to the quantum system. These profiles and mean values arecompared in order to identify the effects of post-selection upon projectormeasurement pointers. As a special case, these mean value results are appliedto the weak measurement regime - yielding PS and PPS mean value expressionswhich are valid for any operator (projector or non-projector). Measurementsensitivities which are useful for estimating weak measurement accuracies forPS and PPS systems are also obtained and discussed.