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:2310.20418 · Physical Review A

Multipartite entanglement sudden death and birth in randomized hypergraph states

Vinícius Salem, Alison A. Silva, Fabiano M. Andrade

Published Jan 10, 2024• 5 citations
arXivHTMLPDF

Abstract

We introduce and analyze the entanglement properties of randomized hypergraph (RH) states, as an extended notion of the randomization procedure in the quantum logic gates for the usual graph states, recently proposed in the literature. The probabilities of applying imperfect generalized controlled-$Z$ gates simulate the noisy operations over the qubits. We obtain entanglement measures as negativity, concurrence, and genuine multiparticle negativity, and show that entanglement exhibits a nonmonotonic behavior in terms of the randomness parameters, which is a consequence of the nonuniformity of the associated hypergraphs, reinforcing the claim that the entanglement of randomized graph states is monotonic since they are related to 2-uniform hypergraphs. Moreover, we observed the phenomena of entanglement sudden death and entanglement sudden birth in RH states. This work reveals a connection between the nonuniformity of hypergraphs and loss of entanglement.

DOI
10.1103/physreva.109.012416

Related papers

Randomized Hypergraph States and Their Entanglement Properties

Vinícius Salem, Alison A. Silva, Fabiano M. Andrade

ABSTRACT We study the entanglement properties of randomized mixed hypergraph states, extending the concept of randomized mixed graph states to encompass hypergraph‐based quantum states. In our model, imperfect generalized multi‐qubit gates are applied probabilistically, simulating experimentally realistic noisy gate operations where gate fidelity decreases with increasing hyperedge order. We analyze bipartite and genuine multipartite entanglement of these mixed multi‐qubit states. Numerical results for various hypergraph configurations with up to four qubits reveal rich, sometimes nonmonotonic entanglement behavior stemming from the interplay between hyperedge structure and gate imperfections. We derive analytical expressions for entanglement witnesses based on randomization overlap for new hypergraph families. Our findings contribute to understanding entanglement resilience under gate imperfections, providing insight into the experimental implementation of hypergraph states in noisy quantum devices.

arXiv:2506.20075•Annalen der Physik•Jan 1, 2026•2 citations

Quantum Hypergraph States: A Review

Davide Poderini, Dagmar Bruß, Chiara Macchiavello

Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary (LU) and stochastic local operations with classical communication (SLOCC), the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation (MBQC), and to their non-stabilizer character - quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.

quant-pharXiv:2603.10917•Mar 12, 2026•0 citations

Entanglement of random hypergraph states

You Zhou, Alioscia Hamma

Random quantum states and operations are of fundamental and practical interests. In this paper, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random controlled-Z (CZ) and controlled-controlled-Z (CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law but greatly differ in typicality, namely, the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. We discuss the implications of these results for the onset of entanglement complexity and quantum chaos.

arXiv:2110.07158•Physical Review A•Jul 7, 2022•14 citations

Quantum hypergraph states: a review

Davide Poderini, Dagmar Bruß, Chiara Macchiavello

Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary and stochastic local operations with classical communication, the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation, and to their non-stabilizer character, quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.

Reports on Progress in Physics•Jun 1, 2026•0 citations

Decay of negativity of randomized multiqubit mixed states

Mostafa Mansour, Y. Oulouda, A. Sbiri +1 more

Abstract In this paper, we investigate the decay of entanglement of multiqubit randomized entangled states. We start by introducing separable states of collection of n independent qubits. The randomized entangled mixed states are generated from factorisable initial states by coupling the qubits through randomized entangling operators. The bipartite and multipartite entanglement of randomized states are analyzed by employing respectively the concepts of the negativity and the genuine multiparticle negativity as measures of amount of entanglement. The decreases of the amount of entanglement of randomized entangled mixed states is studied in terms of the noisy parameter p .

Laser Physics•Feb 9, 2021•18 citations

Statistical mechanics of multipartite entanglement in hypergraph states

Paolo Scarafile, Giorgia Trotta, Paolo Facchi +4 more

We investigate multipartite entanglement in a particular family of pure $n$-qubit hypergraph states through a statistical-mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of $2^n$ classical binary spins. In this correspondence, each hypergraph state uniquely corresponds to a classical spin configuration, while temperature serves as a control parameter that continuously interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature. Remarkably, the exponential of the zero-temperature entropy directly gives the number of MMES within the set of hypergraph states. For small system sizes ($n \leq 5$), we perform an exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems ($n = 6$ and $7$), where exact methods become computationally infeasible, we employ simulated annealing and parallel tempering algorithms to efficiently sample the exponentially large state space. Our analysis yields quantitative predictions of the number of MMES and reveals how entanglement is statistically distributed across the sets of hypergraph states. These results establish hypergraph states as an ideal platform for investigating multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in restricted families of quantum states.

quant-pharXiv:2609.24508•Sep 22, 2026•0 citations
We introduce and analyze the entanglement properties of randomized hypergraph (RH) states, as an extended notion of the randomization procedure in the quantum logic gates for the usual graph states, recently proposed in the literature. The probabilities of applying imperfect generalized controlled-ZZZ gates simulate the noisy operations over the qubits. We obtain entanglement measures as negativity, concurrence, and genuine multiparticle negativity, and show that entanglement exhibits a nonmonotonic behavior in terms of the randomness parameters, which is a consequence of the nonuniformity of the associated hypergraphs, reinforcing the claim that the entanglement of randomized graph states is monotonic since they are related to 2-uniform hypergraphs. Moreover, we observed the phenomena of entanglement sudden death and entanglement sudden birth in RH states. This work reveals a connection between the nonuniformity of hypergraphs and loss of entanglement.
ABSTRACT We study the entanglement properties of randomized mixed hypergraph states, extending the concept of randomized mixed graph states to encompass hypergraph‐based quantum states. In our model, imperfect generalized multi‐qubit gates are applied probabilistically, simulating experimentally realistic noisy gate operations where gate fidelity decreases with increasing hyperedge order. We analyze bipartite and genuine multipartite entanglement of these mixed multi‐qubit states. Numerical results for various hypergraph configurations with up to four qubits reveal rich, sometimes nonmonotonic entanglement behavior stemming from the interplay between hyperedge structure and gate imperfections. We derive analytical expressions for entanglement witnesses based on randomization overlap for new hypergraph families. Our findings contribute to understanding entanglement resilience under gate imperfections, providing insight into the experimental implementation of hypergraph states in noisy quantum devices.
Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary (LU) and stochastic local operations with classical communication (SLOCC), the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation (MBQC), and to their non-stabilizer character - quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.
Random quantum states and operations are of fundamental and practical interests. In this paper, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random controlled-Z (CZ) and controlled-controlled-Z (CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law but greatly differ in typicality, namely, the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. We discuss the implications of these results for the onset of entanglement complexity and quantum chaos.
Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite entanglement. In this review, we provide a compact overview of the formal structure, entanglement characteristics, and operational relevance of hypergraph states in quantum information theory. We begin by introducing their mathematical foundations and generalizations of the stabilizer formalism. A central focus is placed on their entanglement properties, including the classification under local unitary and stochastic local operations with classical communication, the quantification of multipartite entanglement, and detection techniques via entanglement witnesses. We also explore other nonclassical features of hypergraph states, such as contextuality and genuine multipartite nonlocality, derived from stabilizer-based Bell-type inequalities. Additional attention is given to the role of hypergraph states in error correction, and as a computational resource in measurement-based quantum computation, and to their non-stabilizer character, quantified via resource-theoretic measures of quantum magic. Finally we review their generalization to higher dimensions, i.e. to qudits and continuous variables.
Abstract In this paper, we investigate the decay of entanglement of multiqubit randomized entangled states. We start by introducing separable states of collection of n independent qubits. The randomized entangled mixed states are generated from factorisable initial states by coupling the qubits through randomized entangling operators. The bipartite and multipartite entanglement of randomized states are analyzed by employing respectively the concepts of the negativity and the genuine multiparticle negativity as measures of amount of entanglement. The decreases of the amount of entanglement of randomized entangled mixed states is studied in terms of the noisy parameter p .
We investigate multipartite entanglement in a particular family of pure nnn-qubit hypergraph states through a statistical-mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of 2n2^n2n classical binary spins. In this correspondence, each hypergraph state uniquely corresponds to a classical spin configuration, while temperature serves as a control parameter that continuously interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature. Remarkably, the exponential of the zero-temperature entropy directly gives the number of MMES within the set of hypergraph states. For small system sizes (n≤5n \leq 5n≤5), we perform an exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems (n=6n = 6n=6 and 777), where exact methods become computationally infeasible, we employ simulated annealing and parallel tempering algorithms to efficiently sample the exponentially large state space. Our analysis yields quantitative predictions of the number of MMES and reveals how entanglement is statistically distributed across the sets of hypergraph states. These results establish hypergraph states as an ideal platform for investigating multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in restricted families of quantum states.