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arXiv:1305.2818 · Journal of Physics A Mathematical and Theoretical

Entanglement criteria for Dicke states

Marcel Bergmann, Otfried Gühne

Published Sep 6, 2013• 88 citations
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Abstract

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.

DOI
10.1088/1751-8113/46/38/385304

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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.
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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 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.
We present sufficient criteria for the entanglement of three-qubit states. For some special families of states, the criteria are also necessary for the entanglement. They are formulated as simple sets of inequalities for the mean values of certain observables defined as tensor products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with positive partial transpositions. Furthermore, they improve the best known result for the case of W state mixed with the white noise. The efficiency of the criteria is illustrated through several examples.
Recent experiments demonstrate the production of many thousands of neutral atoms entangled in their spin degrees of freedom. We present a criterion for estimating the amount of entanglement based on a measurement of the global spin. It outperforms previous criteria and applies to a wider class of entangled states, including Dicke states. Experimentally, we produce a Dicke-like state using spin dynamics in a Bose-Einstein condensate. Our criterion proves that it contains at least genuine 28-particle entanglement. We infer a generalized squeezing parameter of -11.4(5) dB.
We consider the problem of characterizing genuine multiparticle entanglement for permutationally invariant states using the approach of positive partial transpose mixtures. We show that the evaluation of this necessary biseparability criterion scales polynomially with the number of particles. In practice, it can be evaluated easily up to ten qubits and improves existing criteria significantly. Finally, we show that our approach solves the problem of characterizing genuine multiparticle entanglement for permutationally invariant three-qubit states.
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.