Separability criteria for several classes of $n$-partite quantum states

TL;DR

This paper develops practical criteria to determine the separability and entanglement of various classes of $n$-partite quantum states, including some that are both necessary and sufficient, advancing quantum state analysis.

Contribution

It introduces new practical and some necessary and sufficient separability criteria for different classes of $n$-partite quantum states, including qubits and qudits.

Findings

Derived practical separability criteria for $n$-qubit and $n$-qudit states

Identified criteria that are sufficient for genuine entanglement

Established a necessary and sufficient criterion for a specific class of $n$-partite states

Abstract

In this paper, we mainly discuss the separability of $n$-partite quantum states from elements of density matrices. Practical separability criteria for different classes of $n$-qubit and $n$-qudit quantum states are obtained. Some of them are also sufficient conditions for genuine entanglement of $n$-partite quantum states. Moreover, one of the resulting criteria is also necessary and sufficient for a class of $n$-partite states.