Filtering of higher-dimensional entanglement networks using information volumes

• URL: http://arxiv.org/abs/2106.12508v2
• Date: Thu, 30 Sep 2021 17:37:12 GMT
• Title: Filtering of higher-dimensional entanglement networks using information volumes
• Authors: Shahabeddin M. Aslmarand, Warner A. Miller, Doyeol (David) Ahn, Paul M. Alsing
• Abstract summary: We introduce a novel geometric approach to characterize entanglement relations in large quantum systems. Our approach is inspired by Schumacher's singlet state triangle inequality, which used an entropic-based distance to capture the strange properties of entanglement.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel geometric approach to characterize entanglement relations in large quantum systems. Our approach is inspired by Schumacher's singlet state triangle inequality, which used an entropic-based distance to capture the strange properties of entanglement using geometric-based inequalities. Schumacher uses classical entropy and can only describe the geometry of bipartite states. We extend his approach by using von Neumann entropy to create an entanglement monotone that can be generalized for higher dimensional systems. We achieve this by utilizing recent definitions for entropic areas, volumes, and higher-dimensional volumes for multipartite quantum systems. This enables us to differentiate systems with high quantum correlation from systems with low quantum correlation and differentiate between different types of multi-partite entanglement. It also enables us to describe some of the strange properties of quantum entanglement using simple geometrical inequalities. Our geometrization of entanglement provides new insight into quantum entanglement. Perhaps by constructing well-motivated geometrical structures (e.g. relations among areas, volumes ...), a set of trivial geometrical inequalities can reveal some of the complex properties of higher-dimensional entanglement in multi-partite systems. We provide numerous illustrative applications of this approach, and in particular to a random sample of a thousand density matrices.

Related papers

• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• 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)
• Emergent gravity from the correlation of spin-$\tfrac{1}{2}$ systems coupled with a scalar field [0.0]
  This paper introduces several ideas of emergent gravity, which come from a system similar to an ensemble of quantum spin-$tfrac12$ particles. To derive a physically relevant theory, the model is constructed by quantizing a scalar field in curved space-time.
  arXiv  Detail & Related papers  (2024-05-03T14:34:48Z)
• Entanglement signatures of a percolating quantum system [0.0]
  Entanglement measures have emerged as one of the versatile probes to diagnose quantum phases and their transitions. We show that when the underlying lattice has percolation disorder, free fermions at a finite density show interesting entanglement properties due to massively degenerate ground states.
  arXiv  Detail & Related papers  (2024-03-22T18:00:07Z)
• 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)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. 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)
• Dynamics and Geometry of Entanglement in Many-Body Quantum Systems [0.0]
  A new framework is formulated to study entanglement dynamics in many-body quantum systems. The Quantum Correlation Transfer Function (QCTF) is transformed into a new space of complex functions with isolated singularities. The QCTF-based geometric description offers the prospect of theoretically revealing aspects of many-body entanglement.
  arXiv  Detail & Related papers  (2023-08-18T19:16:44Z)
• 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)
• Sensing quantum chaos through the non-unitary geometric phase [62.997667081978825]
  We propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system is sensed by studying the implications that the system produces in the long-time dynamics of a probe coupled to it.
  arXiv  Detail & Related papers  (2021-04-13T17:24:08Z)
• 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.