Quantum and classical correlations in Bell three and four qubits, related to Hilbert-Schmidt decomposition

TL;DR

This paper investigates quantum and classical correlations in three- and four-qubit Bell states, revealing their maximal entanglement and how quantum correlations diminish to classical ones upon tracing out qubits, using Hilbert-Schmidt decomposition.

Contribution

It extends the analysis of Bell states to three and four qubits, demonstrating their maximal entanglement and correlation properties via Hilbert-Schmidt decomposition.

Findings

Bell states are maximally entangled.

Quantum correlations are lost when tracing over one qubit.

Remaining correlations are classical, as shown by HS decomposition.

Abstract

The present work studies quantum and classical correlations in three qubits and four qubits general Bell states, produced by operating with braid operators on the computational basis of states. The analogies between the general three qubits and four qubits Bell states and that of two qubits Bell states are discussed. The general Bell states are shown to be maximal entangled, i.e., with quantum correlations which are lost by tracing these states over one qubit, remaining only with classical correlations, as shown by HS decomposition.