Geometry of two-qubit evolution and entanglement protection via local operations

The two-qubit pure state evolution under unitary (Hamiltonian) and measurement transformations is conveniently described via a Hopf fibration map, where an S4 sphere is the two-qubit analog of the single-qubit Bloch sphere and entanglement is encoded in an S4 subspace. We show that there exist two-qubit entanglement protection protocols based only on local operations that are as efficient as in the case of a single qubit state protection. We consider several examples related to current or near future experiments in superconducting circuits. We discuss the relevance of such ideas for quantum computing.