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 control of flying qubits based on the quantum stochastic differential equation (QSDE) that describes the input-output process 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 differential equation for the non-unitary state evolution of the standing quantum system, and the outgoing flying-qubit states can be expressed in the form of 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, with which advanced control techniques can be incorporated for practical applications.