Universal scheme for indirect quantum control

We consider a bipartite quantum object, composed of a quantum system and a quantum actuator which is periodically reset. We show that the reduced dynamics of the system approaches unitarity as the reset frequency of the actuator is increased. This phenomenon arises because quantum systems interacting for a short time can impact each other faster than they can become significantly entangled. In the high reset-frequency limit, the effective Hamiltonian describing the system's unitary evolution depends on the state to which the actuator is reset. This makes it possible to indirectly implement a continuous family of effective Hamiltonians on one part of a bipartite quantum object, thereby reducing the problem of indirect control (via a quantum actuator) to the well-studied one of direct quantum control.

Figure 1

Deviation between $H_{\text{eff}}$ and full $\mathcal{S}-\mathcal{A}$ evolution. Shown is the fidelity $F\left(t\right)=\sqrt{\langle \psi \left(t\right)|{\rho }_{\mathcal{S}}\left(t\right)|\psi \left(t\right)\rangle }$ between $|\psi \left(t\right)\rangle =exp(-it{H}_{\text{eff}}/\hslash )|\alpha \rangle$ and ${\rho }_{\mathcal{S}}\left(t\right)$, the reduced state of $\mathcal{S}$ under evolution by (13), for three different resetting rates $f$. (From top to bottom: $f=10\nu , f=5\nu , f=2\nu$.) The initial state of the system ${\rho }_{\mathcal{S}}\left(0\right)=|\alpha \rangle \langle \alpha |$ is coherent with $\alpha =(1+i)/\sqrt{2}$. We set $\nu =\omega , \mathit{n}=(1,0,0)$, and ${\rho }_{\mathcal{A}}=(\mathbb{1}+{\sigma }_x)/2$ for illustration, and chose the switching function as $g(\tau /\delta t)=2\nu {sin}^2(\pi \tau /\delta t)$ [34].