Information gain versus interference in Bohr's principle of complementarity

TL;DR

This paper investigates the wave-particle duality of photons in a Mach-Zehnder interferometer using quantum information theory, revealing how classical and quantum correlations relate to measurement and interference visibility.

Contribution

It introduces a detailed analysis of the relationship between information gain, correlations, and interference, using Zurek's triple model to clarify the quantum and classical aspects of photon behavior.

Findings

Classical correlations align with path distinguishability.

Quantum correlations relate to quantum coherence.

Derived an analytical expression for quantum correlations in separable states.

Abstract

Based on modern quantum measurement theory, we use Zurek's "triple model" to study, from the viewpoint of quantum information theory, the wave and particle nature of a photon in a symmetric Mach-Zehnder interferometer. In the process of quantum measurement, the state of both the system and the detector is not an entangled state but a correlated state. We find that the information gain about the photon is related to the correlations (including classical and quantum correlations) between the photon and the detector. We also derive the relationship between the information gain and the fringe visibility. We find that the classical correlations remain consistent with the path distinguishability and can be used to describe the particle-like property of the photon. Quantum correlations are not exactly the same as fringe visibility, but both can represent the quantum coherence of the photon. Finally, we provide an analytical expression for quantum correlations of one type of two-qubit separable states.