Quantifying the Wave-Particle Duality

JOHN C. MORRISON

Xin Lyu

Abstract Based on the principle that any introduce of entanglement should not improve the limit of simultaneously obtainable information of the particle aspect and the wave aspect, we show that the Shannon entropy is not suitable for quantifying wave-particle duality by giving a counter example in three-path interferometers.

John C. Morrison

Xin Lü

We consider the problem of quantitative wave-particle duality from the perspective of quantum state discrimination. Specifically, we obtain quantifiers of both the particle aspect and the wave aspect from state discrimination. We show that the familiar one-bet duality relation coincides with the relation obtained from considerations of ambiguous discrimination, and the quantifiers suggested by unambiguous discrimination provide us with additional duality relations. In contrast to earlier similar works, the path asymmetry of the interferometer provides the ensemble to be discriminated, and therefore there is no need to introduce which-path detectors.

Rolf E. Hummel

Chang Niu, Sixia Yu

Quantum Fisher information (QFI) plays an important role in quantum metrology, placing the ultimate limit to how precise we can estimate some unknown parameter and thus quantifying how much information we can extract. We observe that both the wave and particle properties within a Mach–Zehnder interferometer can naturally be quantified by QFI. Firstly, the particle property can be quantified by how well one can estimate the a priori probability of the path taken by the particle within the interferometer. Secondly, as the interference pattern is always related to some phase difference, the wave property can be quantified by how well one can estimate the phase parameter of the original state. With QFI as the unified figure of merit for both properties, we propose a more general and stronger wave-particle duality relation than the original one derived by Englert.