Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases

• URL: http://arxiv.org/abs/2508.17154v1
• Date: Sat, 23 Aug 2025 22:23:34 GMT
• Title: Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Abstract summary: Quantum information theory reveals a clear distinction between local and nonlocal correlations through the entanglement across spatially separated subsystems.<n>We provide a sufficient condition for any subspace to be genuinely entangled, enabling the systematic construction of high-dimensional genuinely entangled subspaces.<n>Our construction yields the largest known GES ever obtained from a UBB.<n>We prove that every UBB is indistinguishable under LOCC protocols, underscoring a distinct manifestation of quantum nonlocality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum information theory reveals a clear distinction between local and nonlocal correlations through the entanglement across spatially separated subsystems. The orthogonal complement of an unextendible biseparable basis (UBB) consists entirely of genuine multipartite entangled states, representing the most robust form of such nonlocal correlations. In this letter, we provide a sufficient condition for any subspace to be genuinely entangled, enabling the systematic construction of high-dimensional genuinely entangled subspaces (GESs) from UBBs. Our construction yields the largest known GES ever obtained from a UBB. In fact, every state in this subspace is 1-distillable across every bipartition which is one of the crucial result we obtained. Furthermore, we prove that every UBB is indistinguishable under LOCC protocols, underscoring a distinct manifestation of quantum nonlocality. The UBBs we construct exhibit strong nonlocality in this scenario, making cryptographic protocols secure not only against LOCC-based attacks but also against coordinated group attacks. We introduce a no-go condition that certifies such an extreme form of nonlocality. All previously known UBBs satisfy this condition, which may lead to the misconception that strong nonlocality is an inherent property of every UBB. However, we construct a UBB that violates the no-go condition and exhibits locality across certain bipartitions, challenging conventional notions of unextendibility and nonlocality in multipartite quantum systems.

Related papers

• Quantum Key Distribution Without Shared Reference Frame Under Unital Noise [42.7789646649633]
  We consider a general and practical scenario of quantum key distribution (QKD) over an unknown, stationary, unital qubit channel.<n>We propose two methods to overcome the physical qubit noise and the lack of shared reference frame.
  arXiv  Detail & Related papers  (2026-06-22T12:24:11Z)
• Entanglement-facilitated macroscopic cluster formation in quantum many-body dynamics [42.89492957665636]
  We find that initial-state entanglement suppresses the proliferation of true-vacuum bubbles and stabilises macroscopic connected clusters.<n>Our results establish a connection between initial-state preparation and the preservation of global structures.
  arXiv  Detail & Related papers  (2026-05-21T18:21:14Z)
• Controlling False Discovery in Arbitrarily Structured Hypothesis Spaces via Reproducing Kernels [47.16593717985932]
  We introduce a framework that unifies continuous domains, graphs, and hierarchies under a single algorithm through kernel choice alone.<n>We provide two decision rules which we prove to control the False Discovery Rate (FDR)<n>We validate our method on two sources: spatial locations derived from high-dimensional real-world datasets, and a differential gene expression task utilizing protein-protein interaction graphs.
  arXiv  Detail & Related papers  (2026-05-17T17:42:56Z)
• Genuinely entangled subspaces and strongly nonlocal unextendible biseparable bases in four-partite systems [0.0]
  A set of pure states is an unextendible biseparable basis (UBB)<n>We present an approach for constructing UBB and prove that the UBB established in this way is strongly nonlocal.<n>We also describe the specific orthonormal basis for some genuinely entangled subspaces.
  arXiv  Detail & Related papers  (2026-03-10T00:18:31Z)
• Discrete Adjoint Schrödinger Bridge Sampler [45.568569543075085]
  adjoint matching (AM) excel in continuous domains, but remain unexplored for discrete spaces.<n>We introduce $mathbfdiscreteASBS$, a unified framework that extends AM and adjoint Schrdinger bridge sampler (ASBS) to discrete spaces.<n> Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.
  arXiv  Detail & Related papers  (2026-02-09T03:41:47Z)
• From Directions to Regions: Decomposing Activations in Language Models via Local Geometry [37.50120706345745]
  We leverage Mixture of Factor Analyzers (MFA) as a scalable, unsupervised alternative that models the activation space.<n>MFA decomposes activations into two compositional geometric objects: the region's centroid in activation space, and the local variation from the centroid.<n>We train large-scale MFAs for Llama-3.1-8B and Gemma-2-2B, and show they capture complex, nonlinear structures in activation space.
  arXiv  Detail & Related papers  (2026-02-02T18:49:05Z)
• Conclusive Local State Marking: More Nonlocality With No Entanglement [0.0]
  Nonlocality exhibited by ensembles of composite quantum states is a striking nonclassical feature of quantum theory.<n>We show that certain ensembles of product states can exhibit a stronger form of nonlocality than entangled ensembles traditionally considered highly nonlocal.
  arXiv  Detail & Related papers  (2025-06-11T05:59:42Z)
• Certified Robustness against Sparse Adversarial Perturbations via Data Localization [39.883465335244594]
  We show that a simple classifier emerges from our theory, dubbed Box-NN, which naturally incorporates the geometry of the problem and improves upon the current state-of-the-art in certified robustness against sparse attacks for the MNIST and Fashion-MNIST datasets.
  arXiv  Detail & Related papers  (2024-05-23T05:02:00Z)
• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis [0.0]
  An unextendible biseparable basis (UBB) is a set of pure biseparable states which span a subspace of a given space. We show that there exists a UBB which can demonstrate the phenomenon of strong quantum nonlocality.
  arXiv  Detail & Related papers  (2024-04-08T21:33:17Z)
• All genuinely entangled stabilizer subspaces are multipartite fully nonlocal [0.0]
  We prove that any stabilizer state defined on a genuinely entangled subspace is multipartite fully nonlocal. We also derive a lower bound on genuine nonlocality content of arbitrary multipartite states, opening the door to its experimental estimation.
  arXiv  Detail & Related papers  (2023-12-14T09:09:10Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)
• Unextendibility, uncompletability, and many-copy indistinguishable ensembles [49.1574468325115]
  We show that the complement of any bipartite pure entangled state is spanned by product states which form a nonorthogonal unextendible product basis (nUPB) of maximum cardinality.<n>We also report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing number of mixed states.
  arXiv  Detail & Related papers  (2023-03-30T16:16:41Z)
• Distinguishability-based genuine nonlocality with genuine multipartite entanglement [0.0]
  We study the distinguishability-based genuine nonlocality of a typical type of genuine multipartite entangled states. We show that the cardinality can at least scale down to linear in the local dimension d, with the linear factor l = 1.
  arXiv  Detail & Related papers  (2022-11-04T11:44:30Z)
• Fully non-positive-partial-transpose genuinely entangled subspaces [0.0]
  We provide a construction of multipartite subspaces that are not only genuinely entangled but also fully non-positive-partial-transpose (NPT) Our construction originates from the stabilizer formalism known for its use in quantum error correction.
  arXiv  Detail & Related papers  (2022-03-31T09:11:16Z)
• Proofs of network quantum nonlocality aided by machine learning [68.8204255655161]
  We show that the family of quantum triangle distributions of [DOI40103/PhysRevLett.123.140] did not admit triangle-local models in a larger range than the original proof. We produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.
  arXiv  Detail & Related papers  (2022-03-30T18:00:00Z)
• Demystifying and Generalizing BinaryConnect [22.41391997183786]
  We show that existing quantization algorithms, including post-training quantization, are surprisingly similar to each other. We argue for proximal maps as a natural family of quantizers that is both easy to design and analyze. We propose ProxConnect (PC) as a generalization of BinaryConnect (BC) and we prove its convergence properties.
  arXiv  Detail & Related papers  (2021-10-25T19:07:38Z)

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.