Quantum averages of weak values

Abstract

We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back-reaction on the measured system. We then present a new framework for general measurement conditions (where the back-reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework.

Pre- and post-selection, weak values and contextuality

“…WMs on box C will record the "paradoxical," non-classical outcome of −1. WVs like this outside the eigenvalue spectrum cannot be reproduced from any positive definite probability distribution of eigenvalues [31,14,30].…”

“…• Time-symmetry versus time-asymmetry: The HVT approach utilized in [25] focuses on the probability of post-selection and brings in an element of time-asymmetry, apparently endemic to a Bayesian approach [14].…”

Conditional average in a quantum system with postselection

“…This relation is equivalent to that discussed in Ref. [18], where the correspondence is given by Ŵ f i ↔ p 1b and P suc ( f |i) ↔ P 1b (φ) with p 1b and P 1b (φ) being defined in Ref. [18].…”

“…[18], where the correspondence is given by Ŵ f i ↔ p 1b and P suc ( f |i) ↔ P 1b (φ) with p 1b and P 1b (φ) being defined in Ref. [18]. To show that the average value Ŵ f i of the pointer observable is proportional to the conditional average A f i of the system observableÂ, we assume that the apparatus state |ψ a of the s-part is an eigenstate of the pointer observableX such thatX |ψ a = ga|ψ a and ψ a |ψ a = δ aa with some scaling parameter g. Then we have…”

Test of weak measurement on a two- or three-qubit computer

“…[10]. We will now show that, using just two qubits, we can get perfect quantitative evidence of the weak value as an objective dynamic quantity of the usual sense.…”