Genuine multipartite entanglement measure

• URL: http://arxiv.org/abs/2108.03638v6
• Date: Fri, 11 Feb 2022 11:22:19 GMT
• Title: Genuine multipartite entanglement measure
• Authors: Yu Guo, Yanping Jia, Xinping Li, and Lizhong Huang
• Abstract summary: 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.
• Score: 2.2242717978425257
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Quantifying genuine entanglement is a crucial task in quantum information theory.In this work, we give an approach of constituting genuine $m$-partite entanglement measures from any bipartite entanglement and any $k$-partite entanglement measure, $3\leq k<m$. In addition, as a complement to the three-qubit concurrence triangle proposed in [Phys. Rev. Lett., 127, 040403], we show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.

Related papers

• Scheme of quantum communications based on Witting polytope [55.2480439325792]
  Presented paper describes how to use this configuration for a quantum key distribution protocol based on contextuality using some illustrative examples with 40 "quantum cards" In a more general case, two arbitrary quantum systems with four basis states (ququarts) can be used instead.
  arXiv  Detail & Related papers  (2025-03-24T08:26:48Z)
• Symmetric quantum joint measurements on multiple qubits [0.0]
  We describe a method for constructing a symmetric joint measurement basis for three qubits. We demonstrate the expected tetrahedral symmetry of the current measurement basis. This architecture enables us to generalize the two-qubit symmetric joint measurement to an $n$-qubit version.
  arXiv  Detail & Related papers  (2025-03-12T02:01:46Z)
• Geometric bound on structure factor [44.99833362998488]
  We show that a quadratic form of quantum geometric tensor in $k$-space sets a bound on the $q4$ term in the static structure factor $S(q)$ at small $vecq$.<n> Bands that saturate this bound satisfy a condition similar to Laplace's equation, leading us to refer to them as $textitharmonic bands$.
  arXiv  Detail & Related papers  (2024-12-03T18:30:36Z)
• 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)
• Multipartite entanglement in the diagonal symmetric subspace [41.94295877935867]
  For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$. We present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension.
  arXiv  Detail & Related papers  (2024-03-08T12:06:16Z)
• 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)
• Sequential sharing of two-qudit entanglement based on the entropic uncertainty relation [15.907303576427644]
  Entanglement and uncertainty relation are two focuses of quantum theory. We relate entanglement sharing to the entropic uncertainty relation in a $(dtimes d)$-dimensional system via weak measurements with different pointers.
  arXiv  Detail & Related papers  (2023-04-12T12:10:07Z)
• Multipartite Entanglement: A Journey Through Geometry [0.0]
  Genuine multipartite entanglement is crucial for quantum information and related technologies but quantifying it has been a long-standing challenge. We introduce an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement.
  arXiv  Detail & Related papers  (2023-04-06T17:59:26Z)
• Geometric genuine multipartite entanglement for four-qubit systems [0.0]
  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.
  arXiv  Detail & Related papers  (2022-12-21T16:36:10Z)
• 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)
• Quantum entanglement and contextuality with complexifications of $E_8$ root system [91.3755431537592]
  The Witting configuration with 40 complex rays was suggested as a possible reformulation of Penrose model with two spin-3/2 systems based on geometry of dodecahedron. An analysis of properties of suggested configuration of quantum states is provided using many analogies with properties of Witting configuration.
  arXiv  Detail & Related papers  (2022-10-27T11:23:12Z)
• 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)
• Symmetry and Classification of Multipartite Entangled States [0.0]
  dissertation covers various aspects of entanglement in multipartite states and the role of symmetry in such systems. We establish a connection between the classification of multipartite entanglement and knot theory and investigate the family of states that are resistant to particle loss.
  arXiv  Detail & Related papers  (2022-04-28T12:13:21Z)
• Relative Pose from SIFT Features [50.81749304115036]
  We derive a new linear constraint relating the unknown elements of the fundamental matrix and the orientation and scale. The proposed constraint is tested on a number of problems in a synthetic environment and on publicly available real-world datasets on more than 80000 image pairs.
  arXiv  Detail & Related papers  (2022-03-15T14:16:39Z)

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.