Entanglement detection: Linear entropy versus Bell-CHSH inequality

TL;DR

This paper investigates the relationship between linear entropy and entanglement detection, showing that linear entropy can identify entangled states more effectively than Bell-CHSH inequalities and previous entropic criteria.

Contribution

It establishes a new entanglement criterion based on linear entropy, which detects a broader set of entangled states than Bell-CHSH inequality and prior entropic methods.

Findings

Linear entropy less than 2/3 indicates entanglement.

Linear entropy greater or equal to 2/3 does not guarantee entanglement.

The new criterion detects more entangled states than Bell-CHSH and previous entropic criteria.

Abstract

The relation between the violation of the Bell-CHSH inequalities and entanglement properties of quantum states is not clear so one may consider the mixedness of the system to understand the entanglement properties better than the Bell-CHSH inequality. In this respect, we prove that if the mixedness of the state measured by the linear entropy is less than 2/3 but strictly greater than zero then the two qubit states are entangled. But if the linear entropy is greater or equal to 2/3 then the state may or may not be entangled. Further we show that our entanglement criterion detects larger set of entangled state than Bell-CHSH inequality and Santos's entropic criterion [Phys. Rev. A 69, 022305 (2004)]. Lastly we illustrate our result by citing few examples.