Critical sets of the total variance of state detect all SLOCC entanglement classes

Abstract

We present a general algorithm for finding all classes of pure multiparticle states equivalent under Stochastic Local Operations and Classsical Communication (SLOCC). We parametrize all SLOCC classes by the critical sets of the total variance function. Our method works for arbitrary systems of distinguishable and indistinguishable particles. We also discuss the Morse indices of critical points which have the interpretation of the number of independent non-local perturbations increasing the variance and hence entanglement of a state. We illustrate our method by two examples.

4 pages

References in corpus (1)

• The Pauli principle revisited

Cited by in corpus (35)

• Entanglement in indistinguishable particle systems
• Computable and operationally meaningful multipartite entanglement measures
• When is a pure state of three qubits determined by its single-particle reduced density matrices?
• Entanglement of three-qubit random pure states
• Generalized Pauli constraints in small atoms
• Entanglement classes of permutation-symmetric qudit states: symmetric operations suffice
• Anticoherence measures for pure spin states
• Machine Learning Universal Bosonic Functionals
• Asymptotic properties of entanglement polytopes for large number of qubits
• Lower Bounding Ground-State Energies of Local Hamiltonians Through the Renormalization Group
• Four-qubit pure states as fermionic states
• Role of the pair potential for the saturation of generalized Pauli constraints
• Locally Maximally Entangled States of Multipart Quantum Systems
• Quantum marginals from pure doubly excited states
• Bridging Coherence Optics and Classical Mechanics -- A Universal Light Polarization-Entanglement Complementary Relation
• A link between Quantum Entanglement, Secant varieties and Sphericity
• Entanglement transitivity problems
• Recoupling coefficients and quantum entropies
• Certificates of quantum many-body properties assisted by machine learning
• Critical points of the linear entropy for pure L-qubit states
• Entanglement Classification from a Topological Perspective
• Canonical form of three-fermion pure-states with six single particle states
• A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
• Classification of four qubit states and their stabilisers under SLOCC operations
• Fidelity between a bipartite state and another one undergoing local unitary dynamics
• Introduction to quantum entanglement in many-body systems
• Tripartite Entanglement and Quantum Correlation
• Implications of pinned occupation numbers for natural orbital expansions. II: Rigorous derivation and extension to non-fermionic systems
• Curves in quantum state space, geometric phases, and the brachistophase
• Simple permutation-based measure of quantum correlations and maximally-3-tangled states
• Higher order singular value decomposition and the reduced density matrices of three qubits
• Designing locally maximally entangled quantum states with arbitrary local symmetries
• Non-Locality$\ne$Quantum Entanglement
• Speed excess and total acceleration: a kinematical approach to entanglement
• Special core tensors of multi-qubit states and the concurrency of three lines