A measurement with small information and disturbance per trial, often implemented by coupling an observable weakly to a meter so that its eigenvalue-dependent pointer distributions overlap. Repeated observations can still accumulate substantial measurement backaction. A weak value additionally requires specified preparation and postselection; a weak measurement without postselection need not involve one.
For preselected and nonorthogonal postselected , the displayed transition-amplitude ratio controls the first-order conditional pointer response to a von Neumann measurement interaction. It can be complex or outside an observable's eigenvalue range. Expanding to first order gives , proving that interpretation within the expansion's validity regime.[ref]
Weak values by Yakir Aharonov, David Z. Albert and Lev Vaidman. 1988 primary proposal: weak values in a preselected and postselected spin ensemble
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Weak measurement is a concept in quantum mechanics that allows for the extraction of information about a quantum system without significantly disturbing it. This approach contrasts with traditional (or "strong") measurements, which typically collapse the quantum state of the system into one of its eigenstates and irreversibly alter its properties. In a weak measurement, the interaction between the measuring device and the quantum system is intentionally kept minimal, leading to only a slight disturbance of the system's state.