Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)

Abstract

We propose a new approach to the geometry of the four-qubit entanglement classes depending on parameters. More precisely, we use invariant theory and algebraic geometry to describe various stratifications of the Hilbert space by SLOCC invariant algebraic varieties. The normal forms of the four-qubit classification of Verstraete {\em et al.} are interpreted as dense subsets of components of the dual variety of the set of separable states and an algorithm based on the invariants/covariants of the four-qubit quantum states is proposed to identify a state with a SLOCC equivalent normal form (up to qubits permutation).

49 pages, 16 figures

References in corpus (9)

• Constructing N-qubit entanglement monotones from anti-linear operators
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Four-qubit entanglement from string theory
• On polynomial invariants of several qubits
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• On the geometry of four qubit invariants
• A three-qubit interpretation of BPS and non-BPS STU black holes
• Geometric descriptions of entangled states by auxiliaries varieties
• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case

Cited by in corpus (10)

• Quantum Entanglement involved in Grover's and Shor's algorithms: the four-qubit case
• Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry
• An Algebraic-Geometric Characterization of Tripartite Entanglement
• Geometric approach to entanglement quantification with polynomial measures
• Learning Algebraic Models of Quantum Entanglement
• Hyperdeterminants from the $E_8$ Discriminant
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• Coarse-grained entanglement classification through orthogonal arrays
• Classifying Entanglement by Algebraic Geometry
• Toward Jordan Decompositions of Tensors