Quantum-phase synchronization

TL;DR

This paper investigates how to synchronize the quantum phase of two qubits using unitary operations, revealing conditions for perfect synchronization and optimal fidelity for unknown states.

Contribution

It introduces methods for quantum-phase synchronization, including optimal circuits and conditions for perfect synchronization in specific cases.

Findings

Perfect quantum-phase synchronization is possible for known states.

Maximum average fidelity is achieved with specific quantum circuits.

Perfect synchronization is possible for states on the equatorial plane.

Abstract

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.