Partial separability and entanglement criteria for multiqubit quantum states

TL;DR

This paper develops experimentally accessible criteria based on correlations of local observables to detect various levels of partial separability and entanglement in multiqubit states, outperforming previous criteria and showing robustness against noise.

Contribution

It introduces new inequalities for multiqubit entanglement detection that are stronger, noise-robust, and require fewer measurement settings than existing methods.

Findings

Stronger than several known entanglement criteria.

Robust against noise for various multiqubit states.

Capable of detecting bound entangled states for N ≥ 3.

Abstract

We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial separability in a hierarchical order. These conditions take the form of bounds on the correlations of locally orthogonal observables. Violations of such inequalities give strong sufficient criteria for various forms of partial inseparability and multiqubit entanglement. The strength of these criteria is illustrated by showing that they are stronger than several other well-known entanglement criteria (the fidelity criterion, violation of Mermin-type separability inequalities, the Laskowski-\.Zukowski criterion and the D\"ur-Cirac criterion), and also by showing their great noise robustness for a variety of multiqubit states, including N-qubit GHZ states and Dicke states. Furthermore, for N greater than or equal to 3 they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only N+1. If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the anti-diagonal matrix elements of a state in terms of its diagonal matrix elements.