Nagoya University
Theoretical Elementary Particle Physics Laboratory

Date&Time Wed Jan 13 2021 (13:30 - 14:30)
Speaker
Kazuhisa Ogawa
Affiliation Hokkaido U
Title Complex "variance" in quantum measurement for pre- and post-selected systems
Abstract In quantum mechanics, the outcomes of the measurement of an observable for a preselected system show probabilistic behavior.This probabilistic behavior is evaluated by statistics such as expectation value and variance.On the other hand, the measurement of a observable for pre- and postselected systems was introduced as "weak measurement" by Aharonov et al., in which a complex value called "weak value" is obtained as a quantity corresponding to the expectation value.In this study, we further introduce a quantity called "weak variance" as the quantity corresponding to the variance of the observable for the pre- and postselected systems, and examine its general properties.The weak variance is a complex value and can be understood as a change in the probe wave packet width on the quadrature phase plane in indirect measurement.Furthermore, we show that the weak variance can be expressed as the variance of the quasiprobability distribution for the pre- and postselectied systems.Therefore, our formulation of the weak variance can be considered to be a reasonable definition as a counterpart of the variance for the pre- and postselected systems.
Remarks
Slide/Video