Correlation constraints and the Bloch geometry of two qubits

Abstract

We present a novel inequality on the purity of a bipartite state depending solely on the lengthdifference of the local Bloch vectors. For two qubits this inequality is tight for all marginal states and so extends the previously known solution for the 2-qubit marginal problem. With this inequality we construct a 3-dimensional Bloch model of the 2-qubit quantum state space in terms of Bloch lengths, providing a pleasing visualization of this high-dimensional state space. This allows to characterize quantum states by a strongly reduced set of parameters and to investigate the interplay between local properties of the marginal systems and global properties encoded in the correlations.