We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing $n=2$ or 3 modes. We further numerically investigate the structure of these states and their frustration for $n\ensuremath{\le}7$.We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing $n=2$ or 3 modes. We further numerically investigate the structure of these states and their frustration for $n\ensuremath{\le}7$.

arXiv:0908.0114Physical Review ADec 7, 200917 citations

Conditions for entanglement in spin systems and for multipartite entanglement

Arkaitz Zubiaga

Jan 1, 20120 citations

Maximally multipartite entangled states

Paolo Facchi A, Giuseppe Florio, Giorgio Parisi A +1 more

We introduce the notion of maximally multipartite entangled states of $n$ qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small $n$ are investigated, both analytically and numerically.We introduce the notion of maximally multipartite entangled states of $n$ qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small $n$ are investigated, both analytically and numerically.

arXiv:0710.2868Physical Review AJun 11, 2008176 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.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:2609.24508Sep 22, 20260 citations

Maximal entanglement of bipartite spin states in the context of quantum algebra

K. Berrada, Y. Hassouni

The European Physical Journal DDec 3, 201024 citations

Beyond the Entanglement of Qubit Pairs in Multipartite Systems

S. Shelly Sharma, Naresh Kumar Sharma

Jan 1, 20221 citation

n=2

or 3 modes. We further numerically investigate the structure of these states and their frustration for $n\ensuremath{\le}7$.

We introduce the notion of maximally multipartite entangled states of

n

qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small

n

are investigated, both analytically and numerically.

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.