Towards electron-electron entanglement in Penning traps

Entanglement of isolated elementary particles other than photons has not yet been achieved. We show how building blocks demonstrated with one trapped electron might be used to make a model system and method for entangling two electrons. Applications are then considered, including two-qubit gates and more precise quantum metrology protocols.

Figure 1

(a) $\delta {\omega }_a^{\prime }\sqrt{\mathit{Tt}}$ as a function of $\sqrt{6}\Omega t_3$, for a partially entangled state obtained by a single application of $H_I^{\mathrm{gate}}$, Eq. (10) (resonant case), during a time $t_3$, which for $t_3\simeq 2/(\sqrt{6}\Omega )$ obtains an improvement over the best classical strategy (shot-noise limit, dashed). Also shown is the Heisenberg limit, dotted. (b),(c) Classical trajectory of the relative coordinates $x_{\mathrm{st}}$, $y_{\mathrm{st}}$, $z_{\mathrm{st}}$. All the spatial coordinates are relative to $\sqrt{\hslash /m{\omega }_z}$, and time to $1/{\omega }_z$.