Dynamical discontinuities in repeated weak measurements revealed by complex weak values
Phys. Rev. A 113, 042413 – Published 3 April, 2026
DOI: https://doi.org/10.1103/394k-lj6s
Abstract
This work demonstrates that repeated weak measurements together with postselection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle of the postselected state, which serves as a continuous control parameter. As this angle is varied, the expectation value of the meter observables changes abruptly at the point where the imaginary part of the associated weak value, a complex quantity that arises in weak measurements with postselection, becomes zero. Such nonanalytic behavior emerges only when the weak value is genuinely complex for a range of postselection angles. If the weak value remains purely real for all angles, the dynamics remain smooth. The discontinuity originates from an exchange of stability between fixed points of the nonunitary Kraus operator governing the meter's evolution. Remarkably, despite the absence of a thermodynamic limit, the relaxation time in the vicinity of the discontinuity exhibits universal critical behavior characterized by a critical exponent equal to 1, independent of system parameters. These results establish the weak value as a tunable control parameter capable of inducing nonanalytic dynamical responses and reshaping the stability structure of measurement-induced quantum dynamics.
