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.

Figure 1

Dynamical teleportation and creation of an interaction between two remote systems. (a) The setup consists of two atomic ensembles in constant magnetic fields. A freely propagating light field interacts with both samples and is continuously measured. The result is fed back to the atoms. (b) Illustration of the light-matter interaction in terms of discretized spatially localized light modes.

Figure 2

Fidelity for realizing $H_{\mathrm{A}}$ for ${\Omega }_2=2{\Omega }_1$ and $g=\kappa =1$. The results for implementing $H_{\mathrm{P}}$ are provided in 37. Any evolution under a quadratic Hamiltonian can be realized by combining these two interactions with local rotations [33, 39]. The main panel displays the fidelity for optimal squeezing $r_{\mathrm{opt}}$ versus $e^R$ and ${\Omega }_1\Delta t$. The inset shows the fidelity versus the squeezing of the light for $R=3$. The three curves correspond to ${\Omega }_1\Delta t=100$ (dash-dotted line), ${\Omega }_1\Delta t=300$ (dashed line), and ${\Omega }_1\Delta t=500$ (solid line).