Geometric genuine multipartite entanglement for four-qubit systems
- URL: http://arxiv.org/abs/2212.11690v3
- Date: Fri, 11 Aug 2023 08:19:01 GMT
- Title: Geometric genuine multipartite entanglement for four-qubit systems
- Authors: Ansh Mishra, Soumik Mahanti, Abhinash Kumar Roy, and Prasanta K.
Panigrahi
- Abstract summary: We show that concurrence fill is not monotonic under LOCC, hence not a faithful measure of entanglement.
Though it is not a faithful entanglement measure, it encapsulates an elegant geometric interpretation of bipartite squared concurrences.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Xie and Eberly introduced a genuine multipartite entanglement (GME) measure
`concurrence fill'(\textit{Phys. Rev. Lett., \textbf{127}, 040403} (2021)) for
three-party systems. It is defined as the area of a triangle whose side lengths
represent squared concurrence in each bi-partition. However, it has been
recently shown that concurrence fill is not monotonic under LOCC, hence not a
faithful measure of entanglement. Though it is not a faithful entanglement
measure, it encapsulates an elegant geometric interpretation of bipartite
squared concurrences. There have been a few attempts to generalize GME measure
to four-party settings and beyond. However, some of them are not faithful, and
others simply lack an elegant geometric interpretation. The recent proposal
from Xie et al. constructs a concurrence tetrahedron, whose volume gives the
amount of GME for four-party systems; with generalization to more than four
parties being the hypervolume of the simplex structure in that dimension. Here,
we show by construction that to capture all aspects of multipartite
entanglement, one does not need a more complex structure, and the four-party
entanglement can be demonstrated using \textit{2D geometry only}. The
subadditivity together with the Araki-Lieb inequality of linear entropy is used
to construct a direct extension of the geometric GME to four-party systems
resulting in quadrilateral geometry. Our measure can be geometrically
interpreted as a combination of three quadrilaterals whose sides result from
the concurrence in one-to-three bi-partition, and diagonal as concurrence in
two-to-two bipartition.
Related papers
- Disentangled Representation Learning through Geometry Preservation with the Gromov-Monge Gap [65.73194652234848]
Learning disentangled representations in an unsupervised manner is a fundamental challenge in machine learning.
We propose a novel perspective on disentangled representation learning built on quadratic optimal transport.
We show that geometry preservation can even encourage unsupervised disentanglement without the standard reconstruction objective.
arXiv Detail & Related papers (2024-07-10T16:51:32Z) - A new heuristic approach for contextuality degree estimates and its four- to six-qubit portrayals [0.0699049312989311]
We introduce and describe a new method for finding an upper bound on the degree of contextuality and the corresponding unsatisfied part of a quantum contextual configuration.
While the previously used method based on a SAT solver was limited to three qubits, this new method is much faster and more versatile.
arXiv Detail & Related papers (2024-07-03T08:59:30Z) - 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) - Concurrence triangle induced genuine multipartite entanglement measure [0.0]
We study the quantification of genuine multipartite entanglement (GME) for general multipartite states.
A series of triangles, named concurrence triangles, are established corresponding to inequalities.
The GME measures classify which parts are separable or entangled with the rest ones for non genuine entangled pure states.
arXiv Detail & Related papers (2022-12-14T07:27:38Z) - Implications of sparsity and high triangle density for graph
representation learning [67.98498239263549]
Recent work has shown that sparse graphs containing many triangles cannot be reproduced using a finite-dimensional representation of the nodes.
Here, we show that such graphs can be reproduced using an infinite-dimensional inner product model, where the node representations lie on a low-dimensional manifold.
arXiv Detail & Related papers (2022-10-27T09:15:15Z) - Tripartite entanglement measure under local operations and classical
communication [0.6759148939470331]
We study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement.
Our results shed light on studying genuine entanglement and also reveal the complex structure of multipartite systems.
arXiv Detail & Related papers (2022-10-13T03:39:20Z) - 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) - Genuine multipartite entanglement measure [2.2242717978425257]
We show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension.
For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.
arXiv Detail & Related papers (2021-08-08T14:05:00Z) - Coordinate Independent Convolutional Networks -- Isometry and Gauge
Equivariant Convolutions on Riemannian Manifolds [70.32518963244466]
A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold.
We argue that the particular choice of coordinatization should not affect a network's inference -- it should be coordinate independent.
A simultaneous demand for coordinate independence and weight sharing is shown to result in a requirement on the network to be equivariant.
arXiv Detail & Related papers (2021-06-10T19:54:19Z) - Symmetries and Geometries of Qubits, and their Uses [0.0]
Review of Felix Klein's Erlangen Program for symmetries and geometries.
15 continuous SU(4) Lie generators of two-qubits can be placed in one-to-one correspondence with finite projective geometries.
Extensions are considered for multiple qubits and higher spin or higher dimensional qudits.
arXiv Detail & Related papers (2021-03-25T19:49:22Z)
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.