Triple measurements uncertainty and the distinguishment between the separable and entangled states

TL;DR

This paper investigates the relationship between uncertainty measures and the distinction between separable and entangled states in quantum theory, providing new bounds and interpretations for three observables.

Contribution

It introduces an alternative proof for uncertainty constants involving three observables and links these constants to the ability to distinguish between separable and entangled states.

Findings

Derived tightest uncertainty constants for three observables

Provided a physical interpretation of the uncertainty bounds

Linked uncertainty constants to state separability and entanglement

Abstract

Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for three observables, also with a physical interpretation of the uncertainty constants. Our results show that such constants are intimately connected with the distinguishment between separable and entangled states.