# Bell's Inequality and Entanglement in Qubits

## TL;DR

This paper introduces a new method to evaluate quantum entanglement by linking Bell's inequality violation to concurrence without partial trace, applied to Wen-Plaquette model ground states.

## Contribution

It presents an alternative approach to measure entanglement directly from Bell's inequality violation, avoiding partial trace, and applies it to topological quantum states.

## Key findings

- Wen-Plaquette ground states are maximally entangled.
- Upper bound of Bell's inequality violation relates to topological entanglement entropy.
- Method bridges Bell violation and concurrence in multi-qubit systems.

## Abstract

We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell's inequality without performing a partial trace operation. This proposal is demonstrated by bridging the maximum violation of the Bell's inequality and the concurrence of a pure state in an $n$-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell's inequality to the concurrences of a pure state with respect to different bipartitions.