Weak Value and the Wave-Particle Duality

Abstract: The weak value, introduced by Aharonov et al. to extend the conventional scope of physical observables in quantum mechanics, is an intriguing concept which sheds new light on quantum foundations and is also useful for precision measurement, but it poses serious questions on its physical meaning due to the unconventional features including the complexity of its value. In this paper we point out that the weak value has a direct connection with the wave-particle duality, in the sense that the wave nature manifests itself in the imaginary part while the particle nature in the real part. This is illustrated by the double slit experiment, where we argue, with no conflict with complementarity, that the trajectory of the particle can be inferred based on the weak value without destroying the interference.