Quantum-phase synchronization

We study mechanisms that allow one to synchronize the quantum phase of two qubits relative to a fixed basis. Starting from one qubit in a fixed reference state and the other in an unknown state, we find that contrary to the impossibility of perfect quantum cloning, the quantum-phase can be synchronized perfectly through a joined unitary operation. When both qubits are initially in a pure unknown state, perfect quantum-phase synchronization through unitary operations becomes impossible. In this situation we determine the maximum average quantum-phase synchronization fidelity, the distribution of relative phases and fidelities, and identify optimal quantum circuits that achieve this maximum fidelity. A subset of these optimal quantum circuits enable perfect quantum-phase synchronization for a class of unknown initial states restricted to the equatorial plane of the Bloch sphere.