Quantum-state transmission via a spin ladder as a robust data bus

We explore the physical mechanism to coherently transfer the quantum information of spin by connecting two spins to an isotropic antiferromagnetic spin ladder system as data bus. Due to a large spin gap existing in such a perfect medium, the effective Hamiltonian of the two connected spins can be archived as that of Heisenberg type, which possesses a ground state with maximal entanglement. We show that the effective coupling strength is inversely proportional to the distance of the two spins and thus the quantum information can be transferred between the two spins separated by a longer distance, i.e., the characteristic time of quantum-state transferring linearly depends on the distance.

Figure 1

Two qubits $A$ and $B$ connect to a $(2\times N)$-site spin ladder. The ground state of $H$ with $a$-type connection [Fig. 1a] is singlet (triplet) when $N$ is even (odd), while for $b$-type connection [Fig. 1b], one should have the opposite result.

Figure 2

Schematic illustration of the energy levels of the system. (a) When the connections between two qubits and the medium switch off $(J_0=0)$ the ground states are degenerate. (b) and (c) When $J_0$ switches on, the ground state(s) and the first excited state(s) are either singlet or triplet. This is approximately equivalent to that of two coupled spins.

Figure 3

The spin gaps obtained by numerical method for the systems $L=4$, 5, 6, 7, 8, and 10, with $J=10,20,40$, and $J_0=1$ are plotted, which is corresponding to the magnitude of $J_{\mathrm{eff}}$. It indicates that $J_{\mathrm{eff}}\sim 1∕\left(LJ\right)$.