Weak Values are 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.

16 pages, 4 figures, lots of references; v2 considerably expanded for pedagogical clarity; v3 minor typos fixed

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Cited by in corpus (7)

• Jarzynski-like equality for the out-of-time-ordered correlator
• An even simpler understanding of quantum weak values
• Quantum smoothing for classical mixtures
• Weak values in a classical theory with an epistemic restriction
• Weak Measurement and Two-State-Vector Formalism: Deficit of Momentum Transfer in Scattering Processes
• Past observable dynamics of a continuously monitored qubit
• Gravitational Wave Detection via Weak Measurements Amplification