State space for two qutrits has a phase space structure in its core

Abstract

We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the ``magic'' tetrahedron for bipartite qubits---a magic simplex $\mathcal{W}$. This is obtained via the Weyl group which is a kind of ``quantization'' of classical phase space. We analyze how this simplex $\mathcal{W}$ is embedded in the whole state space of two qutrits and discuss symmetries and equivalences inside the simplex $\mathcal{W}$. Because we are explicitly able to construct optimal entanglement witnesses we obtain the border between separable and entangled states. With our method we find also the total area of bound entangled states of the parameter subspace under intervestigation. Our considerations can also be applied to higher dimensions.