Mainz 2017 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 53: Poster: Quantum Optics and Photonics III

Q 53.47: Poster

Thursday, March 9, 2017, 17:00–19:00, P OG2

Exact zeros of entanglement for arbitrary rank-two mixtures derived from a geometric view of the zero polytope — •Andreas Osterloh — Universität Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg

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 GHZ- and 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.