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

8 pages, no figures

References in corpus (10)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement detection
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Quantum information with Gaussian states
• Separability criteria for genuine multiparticle entanglement
• Secure direct communication using Einstein-Podolsky-Rosen pairs and teleportation
• Classification of multi-qubit mixed states: separability and distillability properties
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Deterministic secure direct communication using GHZ states and swapping quantum entanglement

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