Maximally Entangled State and Bell's Inequality in Qubits

TL;DR

This paper introduces a new method to classify maximally entangled quantum states using concurrences and applies Bell's inequality to analyze their entanglement intensity, demonstrating the approach with seven-qubit states.

Contribution

It proposes a novel classification method for maximally entangled states based on concurrences and links critical points to ground states of the toric code model.

Findings

Bell's inequality bounds relate to ground states of the toric code

Maximally entangled states do not necessarily have local maximum entanglement

Method demonstrated on seven-qubit quantum states

Abstract

A maximally entangled state is a quantum state which has maximum von Neumann entropy for each bipartition. Through proposing a new method to classify quantum states by using concurrences of pure states of a region, one can apply Bell's inequality to study intensity of quantum entanglement of maximally entangled states. We use a class of seven-qubit quantum states to demonstrate the method, where we express all coefficients of the quantum states in terms of concurrences of pure states of a region. When a critical point of an upper bound of Bell's inequality occurs in our quantum states, one of the quantum state is a ground state of the toric code model on a disk manifold. Our result also implies that the maximally entangled states does not suggest local maximum quantum entanglement in our quantum states.