Entanglement monotones connect distinguishability and predictability

Distinguishability and predictability appear in different complementarity relations. Englert and Bergou pointed out the possible connection among distinguishability, predictability, and entanglement. They conjectured that an entanglement measure was hidden between the measures of distinguishability and predictability. Qureshi connected these quantities for a particular trio of measures. In this letter, we define a new entropic distinguishability measure and suggest an entanglement measure as the difference between it and an entropic predictability measure from the literature. An entanglement monotone is defined from the largest value of the distinguishability and the corresponding predictability, provided that the predictability satisfies the criteria already established in the literature. Our results formally connect an entanglement monotone with distinguishability and the corresponding predictability, without appealing to specific measures. (C) 2021 Elsevier B.V. All rights reserved.