Speaker: Helena Braga (UFsCar)
Title: D-7 manifold for two qubits in compact Minkowski space
The entanglement properties as well as the existing criteria such as the partial positive transposition and concurrence when described through an isomorphism of the density operator (for a two-qubit system) in a R³ space provides a quantitave physical understood of the fenomena, This understood became transparent by choosing a subset of X states according to elements of SU(2)⊗U(1)⊗SU(2) group algebra. This quantitative analysis consist of detemining invariant squared distances strongly based on positive partial transposition, in a very similar form as those written in the relativity space-time with a Minkowski metric, s²=t²-r². Similarly to Minkowski diagram it is also possible to divide the space through a conic shaped surface where inside there are separable like states and outside the entangled like ones. This method provides not just the determination of separability but also a measure of quantity of entanglement, and a symmetry based explanation for the existing criteria. In this work we show that the method of distances of entanglement can be aplied to other classes of the subalgebra of X states, in a more general way to any D-7 manifold class and not just the traditional X state.