Geometry of entanglement and separability in Hilbert subspaces of dimension up to three

• URL: http://arxiv.org/abs/2309.05144v2
• Date: Fri, 21 Jun 2024 16:55:51 GMT
• Title: Geometry of entanglement and separability in Hilbert subspaces of dimension up to three
• Authors: Rotem Liss, Tal Mor, Andreas Winter,
• Abstract summary: We show the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our results show which geometrical forms quantum entanglement can and cannot take in low-dimensional subspaces.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding the geometric structure of the pure product states in a given three-dimensional Hilbert subspace, which determines all the possible separable and entangled mixed states over the same subspace. In bipartite systems, we characterise the 14 possible qualitatively different geometric shapes for the set of separable states in any three-dimensional Hilbert subspace (5 classes which also appear in two-dimensional subspaces and were found and analysed by Boyer, Liss and Mor [Phys. Rev. A 95:032308, 2017], and 9 novel classes which appear only in three-dimensional subspaces), describe their geometries, and provide figures illustrating them. We also generalise these results to characterise the sets of fully separable states (and hence the complementary sets of somewhat entangled states) in three-dimensional subspaces of multipartite systems. Our results show which geometrical forms quantum entanglement can and cannot take in low-dimensional subspaces.

Related papers

• 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)
• Classification and Quantification of Entanglement Through Wedge Product and Geometry [0.0]
  We have presented a modified faithful entanglement measure, incorporating the higher dimensional volume and the area elements of the parallelepiped formed by the post-measurement vectors. The measure fine grains the entanglement monotone, wherein different entangled classes manifest with different geometries.
  arXiv  Detail & Related papers  (2022-09-01T13:20:44Z)
• Penrose dodecahedron, Witting configuration and quantum entanglement [55.2480439325792]
  A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose. The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. Two entangled systems with quantum states described by Witting configurations are discussed in presented work.
  arXiv  Detail & Related papers  (2022-08-29T14:46:44Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Symmetric States and Dynamics of Three Quantum Bits [0.0]
  We provide an analysis of pure states in the symmetric sector of three quantum bits for what concerns their entanglement properties, separability criteria and dynamics. We propose a physical set up for the states and dynamics we study which consists of a symmetric network of three spin 1/2 particles under a common driving electro-magnetic field.
  arXiv  Detail & Related papers  (2021-11-13T23:32:15Z)
• Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere [0.0]
  The geometric interpretation of (pseudo)spin 1/2 systems on the Bloch sphere has been appreciated across different areas ranging from condensed matter to quantum information and high energy physics. We here employ a coherence vector description to theoretically characterize a general N-level system on the higher dimensional generalized Bloch (hyper)sphere. We demonstrate that for the N-level case, there is an exterior two-sphere that provides a useful characterization of the system, notably by playing a primary role in determining the Chern number.
  arXiv  Detail & Related papers  (2021-10-13T18:00:01Z)
• Geometric quantification of multiparty entanglement through orthogonality of vectors [0.0]
  We show that post-measurement vectors can yield non-identical set of maximally entangled states. We discuss the trade-off between the local properties namely predictability and coherence with the global property.
  arXiv  Detail & Related papers  (2021-03-06T08:28:07Z)
• The shape of higher-dimensional state space: Bloch-ball analog for a qutrit [0.0]
  We show that it is possible to construct a three dimensional model for the qutrit state space. Besides being of indisputable theoretical value, this opens the door to a new type of representation.
  arXiv  Detail & Related papers  (2020-12-01T15:57:13Z)
• Geometry of Similarity Comparisons [51.552779977889045]
  We show that the ordinal capacity of a space form is related to its dimension and the sign of its curvature. More importantly, we show that the statistical behavior of the ordinal spread random variables defined on a similarity graph can be used to identify its underlying space form.
  arXiv  Detail & Related papers  (2020-06-17T13:37:42Z)
• Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
  We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide. For open boundary condition, we find exotic topological bound-pair edge states with radiative losses. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
  arXiv  Detail & Related papers  (2020-02-24T04:44:12Z)
• 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.