Entanglement Classification via Single Entanglement Measure

Abstract

We show that a single polynomial entanglement measure is enough to verify equivalence between generic $n$-qubit states under Stochastic Local Operations with Classical Communication (SLOCC). SLOCC operations may be represented geometrically by Möbius transformations on the roots of the entanglement measure on the Bloch sphere. Moreover, we show how the roots of the 3-tangle measure classify 4-qubit generic states, and propose a method to obtain the normal form of a 4-qubit state which bypasses the possibly infinite iterative procedure.

18 pages, 3 figures

References in corpus (13)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Aspects of generic entanglement
• Constructing N-qubit entanglement monotones from anti-linear operators
• Entangled three-qubit states without concurrence and three-tangle
• All Maximally Entangled Four Qubits States
• Evaluation of convex roof entanglement measures
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Tangles of superpositions and the convex-roof extension
• Monogamy equalities for qubit entanglement from Lorentz invariance
• Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• State transformations within entanglement classes containing permutation-symmetric states
• Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy

Cited by in corpus (1)

• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity