Maximal violation of Bell inequality for any given two-qubit pure state

TL;DR

This paper derives an explicit formula for the maximum Bell inequality violation for any two-qubit pure state, revealing that only maximally entangled states achieve maximal violation and no mixed states do.

Contribution

It provides an analytical expression for the Bell operator bound for any two-qubit pure state, clarifying violation properties and maximal violations.

Findings

Pure entangled states can violate Bell inequality

Maximal violation occurs only for maximally entangled states

No mixed states can produce maximal violation

Abstract

In the case of bipartite two qubits systems, we derive the analytical expression of bound of Bell operator for any given pure state. Our result not only manifest some properties of Bell inequality, for example which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also give the explicit values of maximal violation for any pure state. Finally we point out that for two qubits systems there is no mixed state which can produce maximal violation of Bell inequality.