Convexity of momentum map, Morse index, and quantum entanglement

DOI10.1142/S0129055X14500044zbMath1290.81011arXiv1208.0556WikidataQ59471873 ScholiaQ59471873MaRDI QIDQ5418951

Adam Sawicki, Michał Oszmaniec, Marek M. Kuś

Publication date: 30 May 2014

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.0556

zbMATH Keywords

Morse theorymaximally entangled statesclassification of entanglementKirwan-Ness stratification

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Index theory for dynamical systems, Morse-Conley indices (37B30) Quantum coherence, entanglement, quantum correlations (81P40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items

Entanglement in indistinguishable particle systems ⋮ Universal points in the asymptotic spectrum of tensors ⋮ Multipartite quantum correlations: symplectic and algebraic geometry approach ⋮ Non-locality ≠ quantum entanglement ⋮ Canonical form of three-fermion pure-states with six single particle states ⋮ Duality of averaging of quantum states over arbitrary symmetry groups revealing Schur–Weyl duality ⋮ Stratified manifold of quantum states, actions of the complex special linear group ⋮ Quantum marginals from pure doubly excited states ⋮ Tensor rank is not multiplicative under the tensor product ⋮ Recoupling coefficients and quantum entropies ⋮ Asymptotic properties of entanglement polytopes for large number of qubits ⋮ Tripartite entanglement and quantum correlation ⋮ Momentum maps for mixed states in quantum and classical mechanics ⋮ Local unitary classification of generalized Bell state sets in C5⊗C5 ⋮ On construction of finite averaging sets for SL(2,C) via its Cartan decomposition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Symplectic geometry of entanglement
• Quantum correlations in systems of indistinguishable particles
• Convexity theorems for varieties invariant under a Borel subgroup
• Convexity properties of the moment mapping
• Kählerian potentials and convexity properties of the moment map
• Convexity properties of the moment mapping. II
• The Pauli principle revisited
• On local invariants of pure three-qubit states
• One-Qubit Reduced States of a Pure Many-Qubit State: Polygon Inequalities
• On detection of quasiclassical states
• Local unitary invariants for multipartite quantum systems
• Geometry of the local equivalence of states
• A Normal form for a Matrix under the Unitary Congruence Group
• A Stratification of the Null Cone Via the Moment Map
• Convexity and Commuting Hamiltonians
• On the Theory of Automorphic Functions of a Matrix Variable I-Geometrical Basis