The quantum marginal problem investigates the compatibility of the eigenvalues of the local and global states of a multipartite quantum system. It is a fundamental problem in quantum information for which the solution is only known for simple cases. We investigate a simpler question of the same flavour: Given the purities of the local states of a multipartite system, what is the maximum purity the global state can achieve? We derive a new inequality that holds for bipartite systems of arbitrary dimensions and gives a complete solution for two qubits. Together with previous findings, this result gives rise to a new representation of the quantum state space – the Bloch ball – of two qubits. We show that this 3-dimensional visualization has various interesting properties regarding geometry and argue why it indeed captures many relevant properties of the full, high-dimensional, state space. Finally we extend this solution to three-qubit states, where we derive tight inequalities on the two- and three-body correlations compatible with a pure state.
You can also follow the seminar online at https://meet.google.com/pfu-awyh-hmz
