Weak value

In quantum mechanics, a "weak value" is a concept that arises in the context of weak measurements, which are a type of measurement that allows observers to extract information about a quantum system with minimal disturbance to the system itself. Weak values are defined in the context of a quantum measurement scenario involving a pre-selected and post-selected ensemble of quantum states.

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For preselected

∣ i ⟩

and nonorthogonal postselected

∣ f ⟩

, 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

⟨ f ∣ exp (- i g A \otimes p /ℏ) ∣ i ⟩

to first order gives

⟨ f ∣ i ⟩ [1 - i g A_{w} p /ℏ]

, proving that interpretation within the expansion's validity regime.^[ref]