Entanglement and separability of qubits systems related to measurement processes, Hilbert-Schmidt(HS)decompositions and general Bell states

TL;DR

This paper introduces a generalized method using Hilbert-Schmidt decompositions to quantify entanglement in multi-qubit systems, analyzing GHZ and Bell states through measurement-based quantum correlations.

Contribution

It presents a more general approach for quantifying entanglement in large n-qubit systems, extending beyond previous bipartite methods.

Findings

Quantified entanglement in GHZ and Bell states.

Demonstrated measurement-based quantum correlations.

Extended entanglement quantification to large multi-qubit systems.

Abstract

Separability and entanglement for n-qubits systems are quantified by using Hilbert-Schmidt (HS) decompositions in which the density matrices are decomposed into various terms representing certain one qubit, two-qubits,and larger qubits measurements. The present method is more general than previous methods for bipartite systems as it can be used for quantification of entanglement for large n-qubits systems.We demonstrate the use of such method by analyzing three qubits GHZ states, and three qubits general Bell states produced by a certain multiplications of Braid operators, operating on the computational basis of states. Quantum correlations are obtained by measuring all qubits of these systems, while a measurement of a part of the system gives only classical correlations. Quantification of entanglement for these systems is given by the use of HS decompositions.