Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Symplectic and algebraic geometry tools have proven to be very useful for the description of quantum correlations. They not only provide a mathematically consistent way of phrasing these problems but also offer an insight which is not available with linear algebra approach. In this talk I will discuss ideas and concepts standing behind these methods. First I will review the connection between symmetries of symplectic manifolds and the momentum map. Then I will study the situation when the considered symplectic manifold is the complex projective space of the multi-particle Hilbert space. In particular I will discuss connections with the Kirwan-Ness stratification and the Brion’s convexity theorem that lead to the concept of the entanglement polytope. Entanglement polytopes have been recently proposed as a way of witnessing multipartite entanglement classes using single particle information. I will present first asymptotic results concerning feasibility of this approach for large number of qubits.