Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy
arXiv:1609.08537 · doi:10.1103/PhysRevA.94.062333
Abstract
Here I present a method how intersections of a certain density matrix of rank two with the zero-polytope can be calculated exactly. This is a purely geometrical procedure which thereby is applicable to obtaining the zeros of SL- and SU-invariant entanglement measures of arbitrary polynomial degree. I explain this method in detail for a recently unsolved problem. In particular, I show how a three-dimensional view, namely in terms of the Boch-sphere analogy, solves this problem immediately. To this end, I determine the zero-polytope of the three-tangle, which is an exact result up to computer accuracy, and calculate upper bounds to its convex roof which are below the linearized upper bound. The zeros of the three-tangle (in this case) induced by the zero-polytope (zero-simplex) are exact values. I apply this procedure to a superposition of the four qubit GHZand W-state. It can however be applied to every case one has under consideration, including an arbitrary polynomial convex-roof measure of entanglement and for arbitrary local dimension.
7 pages, 10 figures, revtex4
References in corpus (9)
- Taming multiparticle entanglement
- Monogamy Inequality in terms of Negativity for Three-Qubit States
- Constructing N-qubit entanglement monotones from anti-linear operators
- Entangled three-qubit states without concurrence and three-tangle
- Three-tangle for mixtures of generalized GHZ and generalized W states
- 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
- Quantitative bound entanglement in two-qutrit states
- Testing the Monogamy Relations via Rank-2 Mixtures