Entanglement monotones connect distinguishability and predictability

TL;DR

This paper explores the theoretical connection between entanglement, distinguishability, and predictability in quantum interference experiments, proposing new measures and proving that an entanglement monotone can be derived from these concepts.

Contribution

It introduces a new entropic distinguishability measure and demonstrates how to define an entanglement monotone from distinguishability and predictability without relying on specific measures.

Findings

Defined a new entropic distinguishability measure

Proposed an entanglement measure as a difference between distinguishability and predictability

Proved the possibility of defining an entanglement monotone from maximum distinguishability and predictability

Abstract

Distinguishability and predictability are part of complementarity relations which apply to two different kinds of interference experiments, with and without a path-detector, respectively. In [Opt. Comm. 179, 337 (2000)], Englert and Bergou pointed out the possible connection between distinguishability, predictability, and entanglement. They even conjectured that an entanglement measure was hidden between the measures of distinguishability and predictability. Here, we push forward this conjecture. We start defining a new entropic distinguishability measure and suggesting an entanglement measure as the difference between this entropic distinguishability and an entropic predictability measure already defined in the literature. Besides, we prove that it is possible to define an entanglement monotone from the largest value of the distinguishability and the corresponding predictability, provided that the predictability satisfy the criteria already established in the literature. Thus, this result formally connects an entanglement monotone with distinguishability and the corresponding predictability, without appealing to specific measures.