Weak Value and Uncertainty Relations based on Quasi-probability Distributions of Quantum Observables

by Mr Jaeha Lee

Wednesday 3 Feb 2016, 13:30 → 14:30 Asia/Tokyo

Main Research Building 433 (RIKEN Wako)

Date: Feb 3 (Mon) Time: 13:30 - Place: Main Research bldg. 433 Speaker: Jaeha Lee (The University of Tokyo) Title: Weak Value and Uncertainty Relations based on Quasi-probability Distributions of Quantum Observables Abstract: We discuss a general prescription for the construction of quasi-joint-probability' (QJP) distributions intended to describe the joint behaviour of an arbitrary pair of (generally non-commuting) quantum observables. In particular, we focus on the L^2 structures induced by the QJP distributions, which are found to provide statistical interpretation of the geometric structures introduced on the space of quantum observables. Aharonov's weak value can then be given a geometric/statistical interpretation as either the orthogonal projection of an observable A on the subspace generated by another observable B, or equivalently, as the conditioning of A given B. Moreover, the Cauchy-Schwarz inequality applied on correlations of two observables leads to novel inequalities interpreted as uncertainty relations for approximation/estimation, in which both the position-momentum and the time-energy uncertainty relations can be treated within a unified framework. See more QHP seminars