Partial K-way Negativities of Pure Four qubit Entangled States

TL;DR

This paper introduces partial K-way negativities as polynomial entanglement monotones to quantify genuine four-partite, tripartite, and bipartite entanglement in pure four-qubit states classified into nine families via SLOCC transformations.

Contribution

It develops a method to measure different levels of entanglement in four-qubit states using partial transposition and local invariants, providing a new tool for entanglement characterization.

Findings

Defines partial K-way negativities for four-qubit states.

Shows these negativities are polynomial functions of local invariants.

Provides a framework to quantify genuine multipartite entanglement.

Abstract

It has been shown by Versraete et. al [F. Versraete, J. Dehaene, B. De Moor, and H. Verschelde, Phys. Rev. A65, 052112 (2002)] that by stochastic local operations and classical communication (SLOCC), a pure state of four qubits can be transformed to a state belonging to one of a set of nine families of states. By using selective partial transposition, we construct partial K-way negativities to measure the genuine 4-partite, tripartite, and bi-partite entanglement of single copy states belonging to the nine families of four qubit states. Partial K-way negativities are polynomial functions of local invariants characterizing each family of states as such entanglement monotones.