The nine ways of four qubit entanglement and their threetangle

Abstract

I calculate the mixed threetangle ${\tau }_3[\rho ]$ for the reduced density matrices of the four-qubit representant states found in Phys. Rev. A {\bf 65}, 052112 (2002). In most of the cases, the convex roof is obtained, except for one class, where I provide with a new upper bound, which is assumed to be very close to the convex roof. I compare with results published in Phys. Rev. Lett. {\bf 113}, 110501 (2014). Since the method applied there usually results in higher values for the upper bound, in certain cases it can be understood that the convex roof is obtained exactly, namely when the zero-polytope where ${\tau }_3$ vanishes shrinks to a single point.

9 pages, 13 figures, revtex 4

References in corpus (12)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Taming multiparticle 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
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• On polynomial invariants of several qubits
• Tangles of superpositions and the convex-roof extension
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• Strong monogamy inequalities for four qubits
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition

Cited by in corpus (6)

• Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
• A Variational Approach to the Quantum Separability Problem
• Realization of the tradeoff between internal and external entanglement
• Generalized W-state of four qubits with exclusively threetangle
• Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy
• Upper bound on three tangles of reduced states of four-qubit pure states