Weak values as interference phenomena

Abstract

Weak values arise experimentally as conditioned averages of weak (noisy) observable measurements that minimally disturb an initial quantum state, and also as dynamical variables for reduced quantum state evolution even in the absence of measurement. These averages can exceed the eigenvalue range of the observable ostensibly being estimated, which has prompted considerable debate regarding their interpretation. Classical conditioned averages of noisy signals only show such anomalies if the quantity being measured is also disturbed prior to conditioning. This fact has recently been rediscovered, along with the question whether anomalous weak values are merely classical disturbance effects. Here we carefully review the role of the weak value as both a conditioned observable estimation and a dynamical variable, and clarify why classical disturbance models will be insufficient to explain the weak value unless they can also simulate other quantum interference phenomena.

Jarzynski-like equality for the out-of-time-ordered correlator

“…(11) can provide an independent bounding method that offers new insights. [45][46][47]. This quasiprobability has been inferred from weak-measurement experiments [50][51][52][53][54].…”

“…Equation (A1) can be derived, e.g., from the Gaussian-meter model [47,63] or the qubit-meter model [56]. The projector can be generalized to a projector v 1 onto a degenerate eigensubspace.…”

“…I first defineà ρ , which resembles the Kirkwood-Dirac quasiprobability [43,[45][46][47]. We gain insight FIG.…”

“…Thisà ρ resembles the Kirkwood-Dirac quasiprobability [43,47]. Quasiprobabilities surface in quantum optics and in the foundations of quantum theory [48,49].…”

“…The Kirkwood-Dirac distribution for a state σ ∈ D(H) has the form f |a a|σ |f , wherein {|f f |} and {|a a|} denote bases for H [47]. Equation (4) has the same form, except it contains more outer products.…”