Spin-state transfer in laterally coupled quantum-dot chains with disorders

Quantum dot arrays are a promising medium for transferring quantum information between two distant points without resorting to mobile qubits. Here we study the two most common disorders, namely hyperfine interaction and exchange coupling fluctuations, in quantum dot arrays and their effects on quantum communication through these chains. Our results show that the hyperfine interaction is more destructive than the exchange coupling fluctuations. The average optimal time for communication is not affected by any disorder in the system and our simulations show that antiferromagnetic chains are much more resistive than the ferromagnetic ones against both kind of disorders. Even when time modulation of a coupling and optimal control is employed to improve the transmission, the antiferromagnetic chain performs much better. We have assumed the quasistatic approximation for hyperfine interaction and time-dependent fluctuations in the exchange couplings. Particularly for studying exchange coupling fluctuations we have considered the static disorder, white noise, and $1/f$ noise.

Figure 1

(a) Scheme for transferring an arbitrary pure state through the quantum dot chain. Spin 0 is the sender qubit and initially is decoupled from the channel qubits (spins $1,2,\dots ,N$) which are prepared in their ground state. The sender places the quantum information on the 0th qubit and switches on the interaction between the 0th and the 1st qubit of the channel in order to send the information to the $N$th qubit. (b) Scheme for entanglement distribution. At the beginning, the channel is initialized to its ground state, and a singlet state is prepared between spin 0 and spin $0^{\prime }$. The sharing entangled information propagates from the 0th spin to the $N$th one by switching on the coupling between the 0th spin and the 1st spin while spin $0^{\prime }$ remains decoupled from the rest of the system during the evolution.

Figure 2

Time evolutions of the average fidelity $\langle F_{\mathrm{av}}\rangle {}_B$ as well as the concurrence $\langle C\rangle {}_B$ in a chain of length $N=10$ in the presence of hyperfine interaction for FM [(a) and (c)] and AFM quantum dot chains [(b) and (d)]. Here $J$ is absolute value of the exchange coupling between two dots.

Figure 3

Comparison of average fidelity $\langle F_{\mathrm{av}}\rangle {}_B$ and concurrence $\langle C\rangle {}_B$ between FM [(a) and (c)] and AFM [(b) and (d)] quantum dot chains in terms of standard deviation $B_{\mathrm{nuc}}$ for different lengths. The red straight solid line represents the highest average fidelity accessible to the classical teleportation scheme.

Figure 4

Comparison of average fidelity $\langle F_{\mathrm{av}}\rangle {}_B$ and concurrence $\langle C\rangle {}_B$ in FM [(a) and (c)] and AFM [(b) and (d)] quantum dot chains as a function of length $N$ for different values of $B_{\mathrm{nuc}}$. The red straight solid line represents the highest average fidelity accessible to the classical teleportation scheme.

Figure 5

Comparison of average fidelity $\langle F_{\mathrm{av}}\rangle {}_J$ and concurrence $\langle C\rangle {}_J$ between FM [(a) and (c)] and AFM [(b) and (d)] chains of length $N=10$ as a function of time for ${\sigma }_J=0.1J$ and different sort of noises such as $\alpha =0$ (white noise), $\alpha =1$ ($1/f$ noise), and $\alpha =\infty$ (static noise). Here $J$ is absolute value of the exchange coupling between two dots.

Figure 6

Average fidelity $\langle F_{\mathrm{av}}\rangle {}_J$ and concurrence $\langle C\rangle {}_J$ in terms of disorder strength ${\sigma }_J$ in both FM [(a) and (c)] and AFM chains [(b) and (d)] for different lengths. The red straight line at $2/3$ shows the fidelity accessible to the classical teleportation scheme.

Figure 7

Average fidelity $\langle F_{\mathrm{av}}\rangle {}_J$ and concurrence $\langle C\rangle {}_J$ versus the length $N$ in both FM [(a) and (c)] and AFM [(b) and (d)] chains for different values of ${\sigma }_J$. The red straight line at $2/3$ shows the fidelity accessible to the classical teleportation scheme.

Figure 8

Average fidelity $\langle F_{\mathrm{av}}\rangle$ and concurrence $\langle C\rangle$ in FM [(a) and (c)] and AFM [(b) and (d)] noisy chains versus both $B_{\mathrm{nuc}}$ and ${\sigma }_J$ in a chain of length $N=8$.

Figure 9

Average fidelity $\langle F_{\mathrm{av}}\rangle$ (a) and concurrence $\langle C\rangle$ (b) in AFM chains versus temperature $T$ in a chain of length $N=6$ in the presence of disorder.

Figure 10

Time evolution of average fidelity $\langle F_{\mathrm{av}}\rangle {}_B$ and concurrence $\langle C\rangle {}_B$ in FM [(a) and (c)] and AFM [(b) and (d)] quantum dot chains with optimal control for different values of $B_{\mathrm{nuc}}$.

Figure 11

Time evolution of average fidelity $\langle F_{\mathrm{av}}\rangle {}_J$ and concurrence $\langle C\rangle {}_J$ in FM [(a) and (c)] and AFM [(b) and (d)] quantum dot chains with optimal control for different values of ${\sigma }_J$.

Figure 12

The spectral density $S(f)$ over 1000 realizations for white noise ($\alpha =0$, red dashed line) and $1/f$ noise ($\alpha =1$, blue solid line). We have set $f_{max}=1000$ and $M=2^{14}$.