2013/10/15 by Jeff Z. Salvail, Salvail, Jeff Z.
Computer Science · Neuroscience · Physics and Astronomy · #FOS: Physical sciences #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1310.4193
5 pages, 2 figures, v2 updated to address anonymous and friendly feedback
openalex publication_date 2013/10/15 · arxiv created 2014/06/03 · arxiv updated 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The AAV effect is the well-known phenomenon where a weak measurement followed by post-selection leads to a pointer shift proportional to the weak value of the measured observable. The effect is usually derived by considering a perturbative expansion of the time-evolution operator corresponding to the measurement. We show that the AAV effect can be instead derived given three simple conditions on the pointer states. The most important condition is that the pointer states be approximately indistinguishable. The other two conditions relate the observables used to characterize the pointer with the measured system observable. This intuitive approach does not require any model for the measurement process, but is completely consistent with the usual approach based on the von Neumann Hamiltonian. Moreover, this approach predicts and explains a new phenomenon, called weak echo, where the usual weak value behaviour can re-emerge at high interaction strengths.