Weak Measurements: Typical Weak and Superweak Values

Abstract

Weak value is a physical property of a quantum system which manifests itself through a weak measurement using different pre-and post-selected ensembles of the system. The weak values of an operator may differ significantly from its eigenvalues and can even lie outside the spectrum if it is bound: they can be 'superweak'. The latter, originating due to a coherent superposition of waves, may appear as a 'supershift' on the measuring device. This property has potential application in the amplification and detection of extremely weak signals.

Weak Measurements: Typical Weak and Superweak Values

“…Recently, the weak value concept was applied to explore the possibility of the apparent superluminal velocity of the neutrinos as a superweak value of the velocity difference operator 13 . Weak values can assist in understanding many counterintuitive quantum results: they can be used as a fundamental test of quantum mechanics by ruling out a class of macro-realistic hidden variable theories, and are equivalent to the violation of generalized Leggett-Garg inequalities 14 , help resolve quantum paradoxes such as Hardy paradox 15 , apparent superluminal travel 16 , and counterfactual problems such as the three-box problem.…”