Natural Parameterization of Two-Qubit States

Abstract

Any pure two-qubit state can be represented by six real angles, with a natural parameterization indicated by the bipartite structure. After explicitly identifying all of these angles for the first time, it is found that the parameters can always be completely separated into two "dynamically local" spinor components. Specifically, given local Hamiltonians at the locations of the two qubits, unitary dynamics on each spinor can be implemented separately without losing any entanglement information in the full state. Such a conclusion also follows from a phase-fixed version of the Schmidt decomposition.