Quantum teleportation of dynamics and effective interactions between remote systems.

Most protocols for quantum information processing consist of a series of quantum gates, which are applied sequentially. In contrast, interactions between matter and fields, for example, as well as measurements such as homodyne detection of light are typically continuous in time. We show how the ability to perform quantum operations continuously and deterministically can be leveraged for inducing nonlocal dynamics between two separate parties. We introduce a scheme for the engineering of an interaction between two remote systems and present a protocol that induces a dynamics in one of the parties that is controlled by the other one. Both schemes apply to continuous variable systems, run continuously in time, and are based on real-time feedback.