Restriction-Based Certificate of Bipartite Schmidt Rank in Hypergraph States

• URL: http://arxiv.org/abs/2602.21016v1
• Date: Tue, 24 Feb 2026 15:34:39 GMT
• Title: Restriction-Based Certificate of Bipartite Schmidt Rank in Hypergraph States
• Abstract summary: Bipartite entanglement in qubit hypergraph states is investigated.<n>Schmidt rank across the cut can be computed as the real rank of a phase-cleaned cross-cut sign matrix.<n>We show that submatrices residual-free bilinear cores yield an exponential Schmidt-rank lower bound in terms of the $mathbbF$-rank of an exposed core matrix.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate bipartite entanglement in qubit hypergraph states across an arbitrary fixed bipartition. Using the real equally weighted (REW) representation, the Schmidt rank across the cut can be computed as the real rank of a phase-cleaned cross-cut sign matrix. Whereas graph states admit an exact cut-rank rule, because the cross-cut phase is purely bilinear, hypergraph states typically contain higher-degree cross-cut interactions, for which the cut-rank rule fails. Our approach certifies entanglement by fixing a single computational-basis assignment on a subset of qubits, thereby selecting a submatrix on an active slice. When this restriction removes all higher-degree cross-cut residues, the remaining cross-cut phase becomes bilinear up to cut-local terms. We call the resulting submatrices residual-free bilinear cores and show that they yield an exponential Schmidt-rank lower bound in terms of the $\mathbb{F}_2$-rank of an exposed core matrix. We further give a combinatorial sufficient condition, phrased as a disjoint bridge matching, that guarantees the existence of large full-rank cores for broad families of CCZ-type bridge patterns, and we present a search-and-verify procedure that constructs and certifies such cores directly from the hyperedge description.

Related papers

• Maximal Classicalization of Finite-Group Quantum Reference-Frame Noise [0.0]
  A finite quantum reference token with group-valued misalignment induces a random-unitary channel.<n>We prove that the following conditions are equivalent for a unitary representation U of a finite group G.
  arXiv  Detail & Related papers  (2026-07-14T17:07:57Z)
• Local large deviations for linear-region growth in random piecewise-linear networks [0.0]
  We study a random compositional model for the growth of affine regions in deep piecewise-linear networks.<n>We prove the existence of a submultiplicative pressure for (N_n), yielding exponential upper bounds for both tails of (n-1log N_n)
  arXiv  Detail & Related papers  (2026-07-08T05:14:19Z)
• Sector-dominant graph-local drivers for path-window barrier Hamiltonians on the Boolean hypercube [0.0]
  We study finite-size adiabatic state preparation on Boolean hypercubes.<n>We use graph-local drivers built from sector/path coordinates related to monotone Gray-code representatives.<n>We provide code, finite certificates, CSV files, validation logs, and reproduction scripts to make the finite-size claims traceable.
  arXiv  Detail & Related papers  (2026-04-28T10:54:42Z)
• Regularized Online RLHF with Generalized Bilinear Preferences [68.44113000390544]
  We consider the problem of contextual online RLHF with general preferences.<n>We adopt the Generalized Bilinear Preference Model to capture preferences via low-rank, skew-symmetric matrices.<n>We prove that the dual gap of the greedy policy is bounded by the square of the estimation error.
  arXiv  Detail & Related papers  (2026-02-26T15:27:53Z)
• Generalized Fusion of Qudit Graph States [0.0]
  We formalize a type-II fusion operation for qudit cluster states within linear optics.<n>Two designated qudits, one from each input cluster, interfere with optional ancilla qudits via a passive linear-optical network.<n>We analyze the probabilities and entanglement of the relevant measurement outcomes, and discuss how our lower bound aligns with existing constructive schemes.
  arXiv  Detail & Related papers  (2025-10-18T19:25:58Z)
• Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective [73.18641268511318]
  We propose a graph-based clustering algorithm that only relaxes the orthonormal constraint to derive clustering results.<n>To ensure a doubly constraint into a gradient, we transform the non-negative constraint into a class probability parameter.
  arXiv  Detail & Related papers  (2025-09-23T09:14:39Z)
• Information-Theoretic Limits and Strong Consistency on Binary Non-uniform Hypergraph Stochastic Block Models [0.0]
  unsupervised classification problem in random hypergraphs under the non-uniform Hypergraph the Block Model (HSBM)<n>In this paper, the information-theoretic limits on the clustering accuracy and the strong consistency threshold are established.
  arXiv  Detail & Related papers  (2023-06-12T03:38:25Z)
• One-step Bipartite Graph Cut: A Normalized Formulation and Its Application to Scalable Subspace Clustering [56.81492360414741]
  We show how to enforce a one-step normalized cut for bipartite graphs, especially with linear-time complexity. In this paper, we first characterize a novel one-step bipartite graph cut criterion with normalized constraints, and theoretically prove its equivalence to a trace problem. We extend this cut criterion to a scalable subspace clustering approach, where adaptive anchor learning, bipartite graph learning, and one-step normalized bipartite graph partitioning are simultaneously modeled.
  arXiv  Detail & Related papers  (2023-05-12T11:27:20Z)
• General Cutting Planes for Bound-Propagation-Based Neural Network Verification [144.7290035694459]
  We generalize the bound propagation procedure to allow the addition of arbitrary cutting plane constraints. We find that MIP solvers can generate high-quality cutting planes for strengthening bound-propagation-based verifiers. Our method is the first verifier that can completely solve the oval20 benchmark and verify twice as many instances on the oval21 benchmark.
  arXiv  Detail & Related papers  (2022-08-11T10:31:28Z)
• Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation [64.49871502193477]
  We propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. Comprehensive experimental results on six commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-05-21T01:47:17Z)
• Exact Recovery in the General Hypergraph Stochastic Block Model [92.28929858529679]
  This paper investigates fundamental limits of exact recovery in the general d-uniform hypergraph block model (d-HSBM) We show that there exists a sharp threshold such that exact recovery is achievable above the threshold and impossible below it.
  arXiv  Detail & Related papers  (2021-05-11T03:39:08Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• Testing correlation of unlabeled random graphs [18.08210501570919]
  We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated. Under the alternative, the two graphs are edge-correlated under some latent node correspondence, but have the same marginal distributions as the null.
  arXiv  Detail & Related papers  (2020-08-23T19:19:45Z)

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.