Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2004.06873 · Physical Review A

Verification of phased Dicke states

Zihao Li, Yun-Guang Han, Hao-Feng Sun, Jiangwei Shang, Huangjun Zhu

Published Feb 3, 2021• 32 citations
arXivHTMLPDF

Abstract

Dicke states are typical examples of quantum states with genuine multipartite entanglement. They are valuable resources in many quantum information processing tasks, including multiparty quantum communication and quantum metrology. Phased Dicke states are a generalization of Dicke states and include antisymmetric basis states as a special example. These states are useful in atomic and molecular physics besides quantum information processing. Here we propose practical and efficient protocols based on adaptive local projective measurements for verifying all phased Dicke states, including $W$ states and qudit Dicke states. To verify any $n$-partite phased Dicke state within infidelity $\ensuremath{\epsilon}$ and significance level $\ensuremath{\delta}$, the number of tests required is only $O(n{\ensuremath{\epsilon}}^{\ensuremath{-}1}ln{\ensuremath{\delta}}^{\ensuremath{-}1})$, which is linear in $n$ and is exponentially more efficient than traditional tomographic approaches. In the case of $W$ states, the number of tests can be further reduced to $O(\sqrt{n}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\epsilon}}^{\ensuremath{-}1}ln{\ensuremath{\delta}}^{\ensuremath{-}1})$. Moreover, we construct an optimal protocol for any antisymmetric basis state; the number of tests required decreases (rather than increases) monotonically with $n$. This is the only optimal protocol known for multipartite nonstabilizer states.

DOI
10.1103/physreva.103.022601

Related papers

Efficient Verification of Dicke States

Ye-Chao Liu, Xiao-Dong Yu, Jiangwei Shang +2 more

Efficient, reliable characterization of quantum states is a basic and important step in most tasks in quantum information processing, but standard approaches, including quantum tomography, are notoriously inefficient. This research offers solutions to the problem of verifying nonstabilizer states by proposing efficient, practical protocols for verifying arbitrary $n$-qubit Dicke states. These protocols require only two distinct settings based on Pauli measurements, and thus are readily applicable with current experimental techniques, and are able to verify the robust Dicke states of hundreds of qubits.

arXiv:1904.01979•Physical Review Applied•Oct 9, 2019•57 citations

Efficient non-tomographic tools for the characterization of multipartite entanglement

Witlef Wieczorek, Nikolai Kiesel, Christoph Schmid +1 more

Entanglement is the crucial resource in the field of quantum information processing and consequently a better understanding of its properties is very desirable. While for bipartite entangled qubit states many tools for characterization exist and also the experimental implementation of the tools is feasible, the situation for multipartite entangled states is different: The available tools have to be suited for a much greater diversity of entanglement properties, e.g. to analyze all the different entanglement classes [1]. A full experimental characterization via state tomography is increasingly difficult as the number of necessary measurement settings grows exponentially with the number of particles. In this contribution we focus on efficient, non-tomographic methods to characterize experimentally observed, multipartite entangled states. First steps towards this goal were demonstrated recently, for instance, for the proof of genuine multipartite entanglement [2] or for the analysis of the persistency of entanglement under loss [3]. Such methods can be further optimized by tailoring them to particular properties of states. We show how three important characteristic quantities, the fidelity, the non-separability and the permutation symmetry, can be evaluated with a significantly lower number of measurement settings than required for a complete tomography. Although the determination of these particular properties provides less information than the reconstruction of the complete density matrix, it allows to judge how well state characteristics are reproduced experimentally. This might be important with respect to an experimental application of states in quantum information. Exemplarily we apply the analysis tools to two genuinely four-qubit entangled states: the Dicke state with two excitations |D 4 〉 [4] and the cluster state |C4 〉 [5, 6]. These states are relevant for particular tasks: The state |D 4 〉 is a resource for telecloning [7], cluster states find an application in one-way quantum computation [6, 8] and are a subgroup of graph states, which play an important role for quantum error correction.

•Jan 1, 2007•0 citations

General framework for verifying pure quantum states in the adversarial scenario

Huangjun Zhu, Masahito Hayashi

Bipartite and multipartite entangled states are of central interest in quantum information processing and foundational studies. Efficient verification of these states, especially in the adversarial scenario, is a key to various applications, including quantum computation, quantum simulation, and quantum networks. However, little is known about this topic in the adversarial scenario. Here we initiate a systematic study of pure-state verification in the adversarial scenario. In particular, we introduce a general method for determining the minimal number of tests required by a given strategy to achieve a given precision. In the case of homogeneous strategies, we can even derive an analytical formula. Furthermore, we propose a general recipe to verifying pure quantum states in the adversarial scenario by virtue of protocols for the nonadversarial scenario. Thanks to this recipe, the resource cost for verifying an arbitrary pure state in the adversarial scenario is comparable to the counterpart for the nonadversarial scenario, and the overhead is at most three times for high-precision verification. Our recipe can readily be applied to efficiently verify bipartite pure states, stabilizer states, hypergraph states, weighted graph states, and Dicke states in the adversarial scenario, even if only local projective measurements are accessible. This paper is an extended version of the companion paper Zhu and Hayashi, Phys. Rev. Lett. 123, 260504 (2019).

arXiv:1909.01943•Physical Review A•Dec 27, 2019•66 citations

Experimentally feasible set of criteria detecting genuine multipartite entanglement in n -qubit Dicke states and in higher-dimensional systems

Marcus Huber, Paul Erker, Hans Schimpf +2 more

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.

arXiv:1011.4579•Physical Review A•Apr 18, 2011•56 citations

Experimental Multipartite Entanglement Detection with Minimal-Size Correlations

Dian Wu, Fei Shi, Jia-Cheng Sun +5 more

Multipartite entanglement is a key resource for quantum technologies, yet its certification typically relies on correlations from measurements involving all particles, making it increasingly vulnerable to imperfections as the system size grows. Here we report the first experimental demonstration of genuine multipartite entanglement detection from correlations with the minimum possible nontrivial support, known as the entanglement detection length (EDL). Using a photonic platform, we certify W, Dicke, and cluster states with entanglement witnesses constructed from correlations at the EDL. In particular, we verify genuine multipartite entanglement of three- and four-qubit W states and a four-qubit Dicke state using two-body correlations, and of a four-qubit cluster state using three-body correlations. For the four-photon Dicke state, we further show that this minimal-correlation strategy is more robust than the compared global witness under the analyzed local-basis-misalignment model. We also find that, within the witness families considered here, increasing the number of measured subsets enhances the tolerance to noise. These results establish entanglement detection at the EDL limit as a measurement-efficient route to multipartite entanglement certification.

arXiv:2510.22918•Physical Review Letters•Jun 9, 2026•0 citations

Multipartite Entanglement Detection with Minimal Effort

Lukas Knips, Christian Schwemmer, Nico Klein +2 more

Certifying entanglement of a multipartite state is generally considered a demanding task. Since an N qubit state is parametrized by 4^{N}-1 real numbers, one might naively expect that the measurement effort of generic entanglement detection also scales exponentially with N. Here, we introduce a general scheme to construct efficient witnesses requiring a constant number of measurements independent of the number of qubits for states like, e.g., Greenberger-Horne-Zeilinger states, cluster states, and Dicke states. For four qubits, we apply this novel method to experimental realizations of the aforementioned states and prove genuine four-partite entanglement with two measurement settings only.

arXiv:1412.5881•Physical Review Letters•Nov 18, 2016•36 citations
Dicke states are typical examples of quantum states with genuine multipartite entanglement. They are valuable resources in many quantum information processing tasks, including multiparty quantum communication and quantum metrology. Phased Dicke states are a generalization of Dicke states and include antisymmetric basis states as a special example. These states are useful in atomic and molecular physics besides quantum information processing. Here we propose practical and efficient protocols based on adaptive local projective measurements for verifying all phased Dicke states, including WWW states and qudit Dicke states. To verify any nnn-partite phased Dicke state within infidelity \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ and significance level \ensuremathδ\ensuremath{\delta}\ensuremathδ, the number of tests required is only O(n\ensuremathϵ\ensuremath−1ln\ensuremathδ\ensuremath−1)O(n{\ensuremath{\epsilon}}^{\ensuremath{-}1}ln{\ensuremath{\delta}}^{\ensuremath{-}1})O(n\ensuremathϵ\ensuremath−1ln\ensuremathδ\ensuremath−1), which is linear in nnn and is exponentially more efficient than traditional tomographic approaches. In the case of WWW states, the number of tests can be further reduced to O(n\ensuremathϵ\ensuremath−1ln\ensuremathδ\ensuremath−1)O(\sqrt{n}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\epsilon}}^{\ensuremath{-}1}ln{\ensuremath{\delta}}^{\ensuremath{-}1})O(n​\ensuremathϵ\ensuremath−1ln\ensuremathδ\ensuremath−1). Moreover, we construct an optimal protocol for any antisymmetric basis state; the number of tests required decreases (rather than increases) monotonically with nnn. This is the only optimal protocol known for multipartite nonstabilizer states.
Efficient, reliable characterization of quantum states is a basic and important step in most tasks in quantum information processing, but standard approaches, including quantum tomography, are notoriously inefficient. This research offers solutions to the problem of verifying nonstabilizer states by proposing efficient, practical protocols for verifying arbitrary nnn-qubit Dicke states. These protocols require only two distinct settings based on Pauli measurements, and thus are readily applicable with current experimental techniques, and are able to verify the robust Dicke states of hundreds of qubits.
Entanglement is the crucial resource in the field of quantum information processing and consequently a better understanding of its properties is very desirable. While for bipartite entangled qubit states many tools for characterization exist and also the experimental implementation of the tools is feasible, the situation for multipartite entangled states is different: The available tools have to be suited for a much greater diversity of entanglement properties, e.g. to analyze all the different entanglement classes [1]. A full experimental characterization via state tomography is increasingly difficult as the number of necessary measurement settings grows exponentially with the number of particles. In this contribution we focus on efficient, non-tomographic methods to characterize experimentally observed, multipartite entangled states. First steps towards this goal were demonstrated recently, for instance, for the proof of genuine multipartite entanglement [2] or for the analysis of the persistency of entanglement under loss [3]. Such methods can be further optimized by tailoring them to particular properties of states. We show how three important characteristic quantities, the fidelity, the non-separability and the permutation symmetry, can be evaluated with a significantly lower number of measurement settings than required for a complete tomography. Although the determination of these particular properties provides less information than the reconstruction of the complete density matrix, it allows to judge how well state characteristics are reproduced experimentally. This might be important with respect to an experimental application of states in quantum information. Exemplarily we apply the analysis tools to two genuinely four-qubit entangled states: the Dicke state with two excitations |D 4 〉 [4] and the cluster state |C4 〉 [5, 6]. These states are relevant for particular tasks: The state |D 4 〉 is a resource for telecloning [7], cluster states find an application in one-way quantum computation [6, 8] and are a subgroup of graph states, which play an important role for quantum error correction.
Bipartite and multipartite entangled states are of central interest in quantum information processing and foundational studies. Efficient verification of these states, especially in the adversarial scenario, is a key to various applications, including quantum computation, quantum simulation, and quantum networks. However, little is known about this topic in the adversarial scenario. Here we initiate a systematic study of pure-state verification in the adversarial scenario. In particular, we introduce a general method for determining the minimal number of tests required by a given strategy to achieve a given precision. In the case of homogeneous strategies, we can even derive an analytical formula. Furthermore, we propose a general recipe to verifying pure quantum states in the adversarial scenario by virtue of protocols for the nonadversarial scenario. Thanks to this recipe, the resource cost for verifying an arbitrary pure state in the adversarial scenario is comparable to the counterpart for the nonadversarial scenario, and the overhead is at most three times for high-precision verification. Our recipe can readily be applied to efficiently verify bipartite pure states, stabilizer states, hypergraph states, weighted graph states, and Dicke states in the adversarial scenario, even if only local projective measurements are accessible. This paper is an extended version of the companion paper Zhu and Hayashi, Phys. Rev. Lett. 123, 260504 (2019).
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.
Multipartite entanglement is a key resource for quantum technologies, yet its certification typically relies on correlations from measurements involving all particles, making it increasingly vulnerable to imperfections as the system size grows. Here we report the first experimental demonstration of genuine multipartite entanglement detection from correlations with the minimum possible nontrivial support, known as the entanglement detection length (EDL). Using a photonic platform, we certify W, Dicke, and cluster states with entanglement witnesses constructed from correlations at the EDL. In particular, we verify genuine multipartite entanglement of three- and four-qubit W states and a four-qubit Dicke state using two-body correlations, and of a four-qubit cluster state using three-body correlations. For the four-photon Dicke state, we further show that this minimal-correlation strategy is more robust than the compared global witness under the analyzed local-basis-misalignment model. We also find that, within the witness families considered here, increasing the number of measured subsets enhances the tolerance to noise. These results establish entanglement detection at the EDL limit as a measurement-efficient route to multipartite entanglement certification.
Certifying entanglement of a multipartite state is generally considered a demanding task. Since an N qubit state is parametrized by 4^{N}-1 real numbers, one might naively expect that the measurement effort of generic entanglement detection also scales exponentially with N. Here, we introduce a general scheme to construct efficient witnesses requiring a constant number of measurements independent of the number of qubits for states like, e.g., Greenberger-Horne-Zeilinger states, cluster states, and Dicke states. For four qubits, we apply this novel method to experimental realizations of the aforementioned states and prove genuine four-partite entanglement with two measurement settings only.