Geometric approach to entanglement quantification with polynomial measures

Entanglement Quantification Made Easy: Polynomial Measures Invariant under Convex Decomposition.

Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are available in only a few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes...

Geometric multipartite entanglement measures

We report on a geometric formulation of multipartite entanglement measures which sets a generalization of the partial formulation of a few-qubit entanglement scenario reported in Ref. [1]. By means of the permutation group of N = 3 elements, we first propose a measure which satisfactorily reproduces the entanglement values reported in the literature for tripartite entangled states. We then give...

Bounding Polynomial Entanglement Measures for Mixed States

Geometric Approach to Digital Quantum Information. Quantum Entanglement. –Senior Project–

The purpose of the project was to attempt an interpretation of the nature of digital quantum information from a geometrical perspective. This lead to designing an algorithm for building the equivalents of Platonic solids in a 2n dimensional Hilbert space, structures called uniform Hilbertian polytopes. The long-term goal was to better understand quantum entanglement, and possibly find a measure...

An introduction to entanglement measures