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:2411.03083

Scalable multipartite entanglement criteria for continuous variables

Xiaoyu Chen

Published Nov 5, 2024• 0 citations
arXivHTMLPDF

Abstract

Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been entangled to build a quantum computer or a quantum simulator, theoretically only for lower dimensional quantum system such as two qubit system or two-mode Gaussian state and some special quantum states, efficient criteria have been developed to detect the entanglement. An efficient and practical entanglement detection method is anticipated to appear for current scalable quantum system. Based on the matched entanglement witness scheme and integrated uncertainty relations, we propose a quite general entanglement detection method for all kinds of multipartite entanglement of multimode continuous variable systems. With the covariance matrix of any randomly generated multimode continuous variable quantum state, our criterion can detect entanglement, genuine entanglement and other kinds of inseparabilities almost imidiately.

DOI
10.48550/arxiv.2411.03083

Related papers

Identifying genuine entanglement of lossy noisy very large scale continuous variable Greenberger-Horne-Zeilinger state

Xiao-yu Chen

Genuine entanglement identification of large scale systems is crucial for quantum computation, quantum communication and quantum learning advantage. In contrast to experiments, where noisy intermediate-scale programmable photonic quantum processors have been developed, theoretically very limited results have been achieved for detecting genuine entanglement of continuous variable multipartite systems. We propose a quite general and efficient entanglement detection framework for all kinds of multipartite entanglement of continuous variable systems based on uncertainty relations and the sign matrix technique. Matrix criteria are demonstrated and can be applied to various entanglement depth and k-separability problems of multimode systems. We illustrate the genuine entanglement conditions of continuous variable Greenberger-Horne-Zeilinger states of more than a hundred million modes in a photon loss and noise environment.

quant-pharXiv:2511.23240•Dec 1, 2025•0 citations

Characterizing the Multipartite Entanglement Structure of Non-Gaussian Continuous-Variable States with a Single Evolution Operator

Mingsheng Tian, Xiaoting Gao, Boxuan Jing +4 more

Multipartite entanglement is an essential resource for quantum information tasks, but characterizing entanglement structures in continuous-variable systems remains challenging, especially in multimode non-Gaussian scenarios. In this Letter, we introduce an efficient method for detecting multipartite entanglement structures in continuous-variable states. Based on the quantum Fisher information, we propose a systematic approach to identify an encoding operator that can efficiently capture the quantum correlations in multimode non-Gaussian states. We demonstrate the effectiveness of our method on over 10^{5} randomly generated multimode-entangled quantum states, achieving a very high success rate in entanglement detection. Additionally, the robustness of our method can be considerably enhanced against losses by expanding the set of accessible operators. This Letter provides a general framework for characterizing entanglement structures in diverse continuous-variable systems, enabling a number of experimentally relevant applications.

arXiv:2408.12554•Physical Review Letters•Sep 4, 2025•5 citations

Matched entanglement witness criteria for continuous variables

Xiaoyu Chen, Maoke Miao, Rui Yin +1 more

We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of Bosonic Gaussian channels. Then we have necessary and sufficient criteria of separability not only for Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from Gaussian states. The criterion can be further explicitly expressed with covariance matrix of the Gaussian state or covariance matrix of Gaussian kernel of the non-Gaussian state. This opens a way for precise detection of non-Gaussian entanglement.

arXiv:2208.12425•Aug 26, 2022•0 citations

Minimal criteria for continuous-variable genuine multipartite entanglement

Olga Leskovjanová, Ladislav Mišta

We derive a set of genuine multi-mode entanglement criteria for second moments of the quadrature operators. The criteria have a common form of the uncertainty relation between sums of variances of position and momentum quadrature combinations. A unique feature of the criteria is that the sums contain the least possible number of variances of at most two-mode combinations. The number of second moments we need to know to apply the criteria thus scales only linearly with the number of modes, as opposed to the quadratic scaling of the already existing criteria. Each criterion is associated with a tree graph, which allowed us to develop a direct method of construction of the criteria based solely on the structure of the underlying tree. The practicality of the proposed criteria is demonstrated by finding a number of examples of Gaussian states of up to six modes, whose genuine multi-mode entanglement is detected by them. The designed criteria are particularly suitable for verification of genuine multipartite entanglement in large multi-mode states or when only a set of two-mode nearest-neighbour marginal covariance matrices of the investigated state is available.

arXiv:2401.04376•Quantum•Aug 27, 2025•3 citations

Improved criteria of detecting multipartite entanglement structure

Kai Wu, Zhihua Chen, Zhen‐Peng Xu +2 more

Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but also the entanglement structure in both fundamental theories and the applications of quantum information technologies. However, it is proved to be challenging to detect the entanglement structures, including entanglement depth, entanglement intactness and entanglement stretchability, especially for general states and large-scale quantum systems. By using the partitions of the tensor product space we propose a systematic method to construct powerful entanglement witnesses which identify better the multipartite entanglement structures. Besides, an efficient algorithm using semi-definite programming and a gradient descent algorithm are designed to detect entanglement structure from the inner polytope of the convex set containing all the states with the same entanglement structure. We demonstrate by detailed examples that our criteria perform better than other known ones. Our results may be applied to many quantum information processing tasks.

arXiv:2406.07274•Jun 11, 2024•0 citations

Entanglement criterion for tripartite systems based on local sum uncertainty relations

Y. Akbari-Kourbolagh, M. Azhdargalam

We propose a sufficient criterion for the entanglement of tripartite systems based on local sum uncertainty relations for arbitrarily chosen observables of subsystems. This criterion generalizes the tighter criterion for bipartite systems introduced by Zhang et al. [C.-J. Zhang, H. Nha, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 81, 012324 (2010)] and can be used for both discrete- and continuous-variable systems. It enables us to detect the entanglement of quantum states without having a complete knowledge of them. Its utility is illustrated by some examples of three-qubit, qutrit-qutrit-qubit, and three-mode Gaussian states. It is found that, in comparison with other criteria, this criterion is able to detect some three-qubit bound entangled states more efficiently.

Physical Review A•Apr 19, 2018•14 citations
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been entangled to build a quantum computer or a quantum simulator, theoretically only for lower dimensional quantum system such as two qubit system or two-mode Gaussian state and some special quantum states, efficient criteria have been developed to detect the entanglement. An efficient and practical entanglement detection method is anticipated to appear for current scalable quantum system. Based on the matched entanglement witness scheme and integrated uncertainty relations, we propose a quite general entanglement detection method for all kinds of multipartite entanglement of multimode continuous variable systems. With the covariance matrix of any randomly generated multimode continuous variable quantum state, our criterion can detect entanglement, genuine entanglement and other kinds of inseparabilities almost imidiately.
Genuine entanglement identification of large scale systems is crucial for quantum computation, quantum communication and quantum learning advantage. In contrast to experiments, where noisy intermediate-scale programmable photonic quantum processors have been developed, theoretically very limited results have been achieved for detecting genuine entanglement of continuous variable multipartite systems. We propose a quite general and efficient entanglement detection framework for all kinds of multipartite entanglement of continuous variable systems based on uncertainty relations and the sign matrix technique. Matrix criteria are demonstrated and can be applied to various entanglement depth and k-separability problems of multimode systems. We illustrate the genuine entanglement conditions of continuous variable Greenberger-Horne-Zeilinger states of more than a hundred million modes in a photon loss and noise environment.
Multipartite entanglement is an essential resource for quantum information tasks, but characterizing entanglement structures in continuous-variable systems remains challenging, especially in multimode non-Gaussian scenarios. In this Letter, we introduce an efficient method for detecting multipartite entanglement structures in continuous-variable states. Based on the quantum Fisher information, we propose a systematic approach to identify an encoding operator that can efficiently capture the quantum correlations in multimode non-Gaussian states. We demonstrate the effectiveness of our method on over 10^{5} randomly generated multimode-entangled quantum states, achieving a very high success rate in entanglement detection. Additionally, the robustness of our method can be considerably enhanced against losses by expanding the set of accessible operators. This Letter provides a general framework for characterizing entanglement structures in diverse continuous-variable systems, enabling a number of experimentally relevant applications.
We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of Bosonic Gaussian channels. Then we have necessary and sufficient criteria of separability not only for Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from Gaussian states. The criterion can be further explicitly expressed with covariance matrix of the Gaussian state or covariance matrix of Gaussian kernel of the non-Gaussian state. This opens a way for precise detection of non-Gaussian entanglement.
We derive a set of genuine multi-mode entanglement criteria for second moments of the quadrature operators. The criteria have a common form of the uncertainty relation between sums of variances of position and momentum quadrature combinations. A unique feature of the criteria is that the sums contain the least possible number of variances of at most two-mode combinations. The number of second moments we need to know to apply the criteria thus scales only linearly with the number of modes, as opposed to the quadratic scaling of the already existing criteria. Each criterion is associated with a tree graph, which allowed us to develop a direct method of construction of the criteria based solely on the structure of the underlying tree. The practicality of the proposed criteria is demonstrated by finding a number of examples of Gaussian states of up to six modes, whose genuine multi-mode entanglement is detected by them. The designed criteria are particularly suitable for verification of genuine multipartite entanglement in large multi-mode states or when only a set of two-mode nearest-neighbour marginal covariance matrices of the investigated state is available.
Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but also the entanglement structure in both fundamental theories and the applications of quantum information technologies. However, it is proved to be challenging to detect the entanglement structures, including entanglement depth, entanglement intactness and entanglement stretchability, especially for general states and large-scale quantum systems. By using the partitions of the tensor product space we propose a systematic method to construct powerful entanglement witnesses which identify better the multipartite entanglement structures. Besides, an efficient algorithm using semi-definite programming and a gradient descent algorithm are designed to detect entanglement structure from the inner polytope of the convex set containing all the states with the same entanglement structure. We demonstrate by detailed examples that our criteria perform better than other known ones. Our results may be applied to many quantum information processing tasks.
We propose a sufficient criterion for the entanglement of tripartite systems based on local sum uncertainty relations for arbitrarily chosen observables of subsystems. This criterion generalizes the tighter criterion for bipartite systems introduced by Zhang et al. [C.-J. Zhang, H. Nha, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 81, 012324 (2010)] and can be used for both discrete- and continuous-variable systems. It enables us to detect the entanglement of quantum states without having a complete knowledge of them. Its utility is illustrated by some examples of three-qubit, qutrit-qutrit-qubit, and three-mode Gaussian states. It is found that, in comparison with other criteria, this criterion is able to detect some three-qubit bound entangled states more efficiently.