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Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states

Tóth, G., Wieczorek, W., Krischek, R., Kiesel, N., Michelberger, P., Weinfurter, H.

Published Aug 4, 2009• 19 citations
OpenAlex

Abstract

We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effort small. We also present general results on the efficient local decomposition of permutationally invariant operators, which makes it possible to measure projectors to symmetric states efficiently.

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We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effort small. We also present general results on the efficient local decomposition of permutationally invariant operators, which makes it possible to measure projectors to symmetric states efficiently.
We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effort small. We also present general results on the efficient local decomposition of permutationally invariant operators, which makes it possible to measure projectors to symmetric states efficiently.
I present methods for detecting entanglement around symmetric Dicke states. In particular, I consider N-qubit symmetric Dicke states with N/2 excitations. I show that for large N these states have the smallest overlap possible with states without genuine multipartite entanglement. Thus these states are particularly well suited for the experimental examination of multipartite entanglement. I present fidelity-based entanglement witness operators for detecting multipartite entanglement around these states. I then consider entanglement criteria, somewhat similar to the spin squeezing criterion, based on the moments or variances of the collective spin operators. Surprisingly, these criteria are based on an upper bound for variances for separable states. I present criteria detecting entanglement in general and criteria detecting only genuine multipartite entanglement. The collective operator measured for this criteria is an important physical quantity: Its expectation value essentially gives the intensity of the radiation when a coherent atomic cloud emits light.
We present methods for detecting entanglement around N-qubit Dicke states with N/2 excitations. In the first part of the paper we show that for large N these states have the smallest overlap possible with states without multi-partite entanglement. Thus these states are particulary well suited for experiments aimed to create and detect genuine multi-partite entanglement. We present fidelity-based entanglement witness operators for detecting multipartite entanglement around these states. In the second part of the paper we consider entanglement criteria, somewhat similar to spin squeezing, based on the moments or variances of the collective spin operators. We present both criteria detecting entanglement in general and criteria detecting only genuine multi-partite entanglement.