Generation of entangled channels for perfect teleportation using multielectron quantum dots

We propose a scheme for generating $N$-qubit entangled states which can teleport an unknown state perfectly. By switching on the exchange interaction $\left(J\right)$ between the qubits one can get the desired states periodically. A multielectron quantum dot can be a possible realization for generating such $N$-qubit states with high fidelity. It is shown that, in the limit of $N\to \infty$, there exists a unique time $t=\frac{2}{3J}{\cos }^{-1}(-1∕8)$, where the Hamiltonian dynamics gives the $N$-qubit state that can carry out perfect teleportation. We also discussed the effect of the nuclear spin environment on the entanglement of the $N$-qubit teleportation channels.

Figure 1

(Color online) Representation of closed and open chains for three and four qubits interacting through Heisenberg exchange interaction. For $\Delta =1$ the chain is perfectly closed and $\Delta =0$ the chain is open.

Figure 2

(Color online) We plot Eq. (9) as a function of time. The times at which the curves intersect with the horizontal line are the solutions to the nonlinear equation given in Eq. (9). The asymmetry parameter $\Delta$ is varied from 0 (open) to 1 (perfectly closed). The times at which one can find solutions to Eq. (9) increases with decreasing $\Delta$.

Figure 3

(Color online) We have plotted Eq. (20) as a function of time for different values of $N$. The times at which the curves intersect with the horizontal line are the solutions to the nonlinear equation given in the above equation. In large $N$ limit, there are no strong revivals indicating that there can exist only one solution corresponding to the first intersection with the horizontal line. Though for finite $N$ there will always be revivals, the revival time increase drastically with $N$.