An algebraic classification of entangled states

Abstract

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes.

published version

References in corpus (4)

• Experimental multiparticle entanglement dynamics induced by decoherence
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Four-qubit entanglement from string theory
• Black Holes, Qubits and Octonions

Cited by in corpus (9)

• SLOCC classification of n qubits invoking the proportional relationships for spectrums and for standard Jordan normal forms
• On the Black-Hole/Qubit Correspondence
• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry
• A comparison of parallel and anti-parallel two qubit mixed states
• Classification of four qubit states and their stabilisers under SLOCC operations
• Coarse-grained entanglement classification through orthogonal arrays
• Classifying Entanglement by Algebraic Geometry
• Entanglement classification via integer partitions