Entanglement in the Dicke subspace

• URL: http://arxiv.org/abs/2602.15800v1
• Date: Tue, 17 Feb 2026 18:39:30 GMT
• Title: Entanglement in the Dicke subspace
• Authors: Aabhas Gulati, Ion Nechita, Clément Pellegrini,
• Abstract summary: We provide a complete mathematical theory for the entanglement of mixtures of Dicke states.<n>These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we provide a complete mathematical theory for the entanglement of mixtures of Dicke states. These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles. We introduce a tensor-based parametrization where the diagonal entries of these states are encoded as a symmetric tensor, enabling a direct translation between entanglement properties and well-studied convex cones of tensors. Our results bridge multipartite entanglement theory with semialgebraic geometry and the theory of completely positive and copositive tensors. This dictionary maps separability to completely positive tensors, the PPT property to moment tensors, entanglement witnesses to copositive tensors, and decomposable witnesses to sum of squares tensors. Using this framework, we construct explicit PPT entangled states in three or more qutrits. In this class of states, we establish that PPT entanglement exists for all multipartite systems with three qutrits or more, disproving a recent conjecture in [J. Math. Phys. 66, 022203 (2025)]. We also show that, for mixtures of Dicke states, the PPT condition with respect to the most balanced bipartition implies PPT with respect to any other bipartition. We further connect bosonic extendibility of mixtures of Dicke states to the duals of known hierarchies for non-negative polynomials, such as the ones by Reznick and Polya. We thus provide semidefinite programming relaxations for separability and entanglement testing in the Dicke subspace.

Related papers

• Tensors, entanglement, separability, and their complexity [0.0]
  Most geometric measure entangled $d$-partite state has minimum spectral norm and maximum nuclear norm.<n>We introduce the notion of Hermitian and density tensors, and the subspace of bi-symmetric Hermitian tensors, which correspond to Bosons.<n>We show that separable density tensors, and strongly separable bi-symmetric density tensors are characterized by the value (equal to one) of their corresponding nuclear norms.
  arXiv  Detail & Related papers  (2025-09-25T21:58:44Z)
• Emergent statistical mechanics in holographic random tensor networks [41.99844472131922]
  We show that RTN states equilibrate at large bond dimension and also in the scaling limit for three classes of geometries.<n>We reproduce a holographic degree-of-freedom counting for the effective dimension of each system.<n>These results demonstrate that RTN techniques can probe aspects of late-time dynamics of quantum many-body phases.
  arXiv  Detail & Related papers  (2025-08-22T17:49:49Z)
• Entanglement in cyclic sign invariant quantum states [0.40964539027092906]
  We study bipartite quantum states that are invariant under the local action of the cyclic sign group.<n>Their important semi-definite properties, such as positivity and positivity under partial transpose (PPT), can be simply characterized in terms of these vectors.
  arXiv  Detail & Related papers  (2025-01-08T19:03:18Z)
• Tensor cumulants for statistical inference on invariant distributions [49.80012009682584]
  We show that PCA becomes computationally hard at a critical value of the signal's magnitude. We define a new set of objects, which provide an explicit, near-orthogonal basis for invariants of a given degree. It also lets us analyze a new problem of distinguishing between different ensembles.
  arXiv  Detail & Related papers  (2024-04-29T14:33:24Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Classification of Dipolar Symmetry-Protected Topological Phases: Matrix Product States, Stabilizer Hamiltonians and Finite Tensor Gauge Theories [0.0]
  We classify one-dimensional symmetry-protected topological phases protected by dipole symmetries. For each phase in the classification, we explicitly construct a stabilizer Hamiltonian to realize the SPT phase. These field theories generalize the Dijkgraaf-Witten theories to twisted finite tensor gauge theories.
  arXiv  Detail & Related papers  (2023-11-08T19:00:00Z)
• The $\mathfrak S_k$-circular limit of random tensor flattenings [1.2891210250935143]
  We show the convergence toward an operator-valued circular system with amalgamation on permutation group algebras. As an application we describe the law of large random density matrix of bosonic quantum states.
  arXiv  Detail & Related papers  (2023-07-21T08:59:33Z)
• Dilute neutron star matter from neural-network quantum states [58.720142291102135]
  Low-density neutron matter is characterized by the formation of Cooper pairs and the onset of superfluidity. We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and reconfiguration techniques.
  arXiv  Detail & Related papers  (2022-12-08T17:55:25Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)

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.