On the Control of Flying Qubits.

The control of flying quantum bits (qubits) carried by traveling quantum fields is crucial for coherent information transmission in quantum networks. In this paper, we develop a general framework for modeling the generation, catching and transformation processes of flying qubits. We introduce the quantum stochastic differential equation (QSDE) to describe the flying-qubit input-output relations actuated by a standing quantum system. Under the continuous time-ordered photon-number basis, the infinite-dimensional QSDE is reduced to a low-dimensional deterministic non-unitary differential equation for the state evolution of the standing system, and the outgoing flying-qubit states can be calculated via randomly occurring quantum jumps. This makes it possible, as demonstrated by examples of flying-qubit generation and transformation, to analyze general cases when the number of excitations is not reserved. The proposed framework lays the foundation for the design of flying-qubit control systems from a control theoretic point of view, within which advanced control techniques can be incorporated for practical applications.