Teleportation of Electronic Many-Qubit States Encoded in the Electron Spin of Quantum Dots via Single Photons

We propose a teleportation scheme that relies only on single-photon measurements and Faraday rotation, for teleportation of many-qubit entangled states stored in the electron spins of a quantum dot system. The interaction between a photon and the two electron spins, via Faraday rotation in microcavities, establishes Greenberger-Horne-Zeilinger entanglement in the spin-photon-spin system. The appropriate single-qubit measurements, and the communication of two classical bits, produce teleportation. This scheme provides the essential link between spintronic and photonic quantum information devices by permitting quantum information to be exchanged between them.

Figure 1

Teleportation of the many-qubit state located initially in the quantum dot system $D$ to the quantum dot system $D^{\prime }$. Each quantum dot of $D$ at ${\mathbf{r}}_j$ is connected to the quantum dot of $D^{\prime }$ at ${\mathbf{r}}_j^{\prime }$ through the photon $j$. This requirement can be satisfied using quantum dots of different sizes, where each pair of dots at ${\mathbf{r}}_j$ and ${\mathbf{r}}_j^{\prime }$ have the same size. Then each pair of dots can be connected by a photon with the proper resonant frequency. Another approach could use fiber optics to ensure a unique connection between each pair of dots at ${\mathbf{r}}_j$ and ${\mathbf{r}}_j^{\prime }$. The independent single-spin detection apparatus is sketched in Fig. 2.

Figure 2

Teleportation of the many-qubit state can be regarded as the independent teleportation of each spin state from ${\mathbf{r}}_j$ to ${\mathbf{r}}_j^{\prime }$, mediated by photons traveling in the $-z$ direction. Each dot is embedded in a microcavity with different lengths in $z$ and $x$, so that the scattered photon cannot change its direction. Single-spin detection is performed by photons propagating along $x$. All the photons are measured independently from each other.

Figure 3

Selection rules for a photon propagating in the $z$ direction and an excess spin-$\uparrow$ electron in the dot. ${\sigma }_{(z)}^{+}$ can be virtually absorbed (upper right) by exciting an electron and a heavy hole, and ${\sigma }_{(z)}^{-}$ by exciting an electon and a light hole (lower left). $\hslash {\omega }_d$ is the detuning of the nonresonant photon.