Path Predictability and Quantum Coherence in Multi-Slit Interference

TL;DR

This paper introduces a new measure of path predictability in multi-slit interference experiments and establishes a duality relation with quantum coherence, extending the two-slit predictability-visibility inequality to multiple slits.

Contribution

It proposes a novel definition of predictability for multi-slit interference and demonstrates a duality relation with quantum coherence that generalizes previous two-slit results.

Findings

New predictability measure for multi-slit interference

Duality relation P^2 + C^2 ≤ 1 for pure states

Reduces to known two-slit relation when applicable

Abstract

In an asymmetric multislit interference experiment, a quanton is more likely to pass through certain slits than some others. In such a situation one may be able to predict which slit a quanton is more likely to go through, even without using any path-detecting device. This allows one to talk of path predictability. It has been shown earlier that for a two-slit interference, the predictability and fringe visibility are constrained by the inequality $P^2+V^2\le 1$. Generalizing this relation to the case of more than two slits is still an unsolved problem. A new definition for predictability for multi-slit interference is introduced. It is shown that this predictability and quantum coherence follow a duality relation $P^2+C^2\le 1$, which saturates for all pure states. For the case of two slits, this relation reduces to the previously known one.