Quantifying the dimensionality of multiparticle entanglement via partition rank

• URL: http://arxiv.org/abs/2608.23399v1
• Date: Mon, 24 Aug 2026 15:46:45 GMT
• Title: Quantifying the dimensionality of multiparticle entanglement via partition rank
• Abstract summary: We introduce a concept to characterize the entanglement dimensionality of multiparticle states based on decompositions of pure states into superpositions of states without genuine multiparticle entanglement.<n>This allows the identification of novel maximally correlated states as well as a discrete classification of quantum states under local operations and classical communication.
• Score: 0.05249805590164902
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The usefulness of entanglement as a resource in quantum technologies increases for larger systems, that is, if more particles or higher-dimensional quantum systems are considered. Yet, the interplay between dimensionality and multiparticle entanglement is not well understood. Only for two-particle systems an unambiguous and coherent notion of entanglement dimensionality, based on the Schmidt decomposition, is known. We introduce a concept to characterize the entanglement dimensionality of multiparticle states based on decompositions of pure states into superpositions of states without genuine multiparticle entanglement. We provide constructive methods to characterize the resulting partition rank for pure and mixed states. This allows the identification of novel maximally correlated states as well as a discrete classification of quantum states under stochastic local operations and classical communication. From a mathematical perspective, our approach can be formulated in terms of the slice rank and partition rank of tensors and our results allow to characterize these by connecting them to a generalized injective tensor norm.

Related papers

• Observable measures of multipartite entanglement [0.0]
  We construct observable bounds to multipartite entanglement for systems of arbitrary size.<n>First, we derive experimentally accessible limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems.<n>We then convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement.
  arXiv  Detail & Related papers  (2026-05-02T10:55:27Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Complete Hierarchies for the Geometric Measure of Entanglement [1.5996418916922266]
  In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces.<n>This product structure leads to the distinction between product states and entangled states.<n>One can quantify entanglement by considering the distance of a quantum state to the set of product states.
  arXiv  Detail & Related papers  (2026-01-30T18:12:55Z)
• Entanglement witnesses for stabilizer states and subspaces beyond qubits [0.0]
  Genuine multipartite entanglement is arguably the most valuable form of entanglement in the multipartite case.<n>In order to detect that form of entanglement in multipartite quantum states, one typically uses entanglement witnesses.<n>We show that the obtained witnesses detecting genuine multipartite entanglement in quantum systems of higher local dimension are superior in terms of noise robustness to those derived for multiqubit states.
  arXiv  Detail & Related papers  (2025-08-19T11:12:11Z)
• Quantum-aware Transformer model for state classification [0.0]
  We present a data-driven approach to entanglement classification using transformer-based neural networks.<n>Our dataset consists of a diverse set of bipartite states, including pure separable states, Werner entangled states, general entangled states, and maximally entangled states.<n>Our method achieves near-perfect classification accuracy, effectively distinguishing between separable and entangled states.
  arXiv  Detail & Related papers  (2025-02-28T13:56:48Z)
• Absolute dimensionality of quantum ensembles [41.94295877935867]
  The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis.<n>We propose an absolute, i.e.basis-independent, notion of dimensionality for ensembles of quantum states.
  arXiv  Detail & Related papers  (2024-09-03T09:54:15Z)
• A nonlinear criterion for characterizing high-dimensional multipartite entanglement [1.8749305679160366]
  We derive a nonlinear criterion that can be used to lower bound the dimensionality vector of mixed quantum states. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect Greenberger-Horne-Zeilinger (GHZ) states.
  arXiv  Detail & Related papers  (2024-05-06T08:33:46Z)
• Relativistic Quantum Fields Are Universal Entanglement Embezzlers [41.94295877935867]
  Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system.<n>We uncover a deep connection between the operational task of embezzling entanglement and the mathematical classification of von Neumann algebras.
  arXiv  Detail & Related papers  (2024-01-14T13:58:32Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.