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Detection of multipartite entanglement in the vicinity of Dicke states with many excitations

Géza Tóth

Published Nov 25, 2005• 0 citations
OpenAlex

Abstract

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.

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We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in $n$-qubit Dicke states with $m$ excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.

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Entanglement criteria for Dicke states

Marcel Bergmann, Otfried Gühne

Dicke states are a family of multi-qubit quantum states with interesting entanglement properties and they have been observed in many experiments. We construct entanglement witnesses for detecting genuine multiparticle entanglement in the vicinity of these states. We use the approach of positive partial transpose mixtures to derive the conditions analytically. For nearly all cases, our criteria are stronger than all conditions previously known.

arXiv:1305.2818•Journal of Physics A Mathematical and Theoretical•Sep 6, 2013•88 citations
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.
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.
Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantify the entanglement depth of many-body systems and is easy to implement as it requires measurement of only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits.
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.
We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in nnn-qubit Dicke states with mmm excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.