Transferring entangled states through spin chains by boundary-state multiplets

Quantum spin chains may be used to transfer quantum states between elements of a quantum information processing device. A scheme discovered recently [Phys. Rev. A 85, 022312 (2012)] was shown to have favorable transfer properties for single-qubit states even in the presence of built-in static disorder caused by manufacturing errors. We extend that scheme in a way suggested already in Bruderer et al. [Phys. Rev. A 85, 022312 (2012)] and study the transfer of the four Bell states which form a maximally entangled basis in the two-qubit Hilbert space. We show that perfect transfer of all four Bell states separately and of arbitrary linear combinations may be achieved for chains with hundreds of spins. For simplicity we restrict ourselves to systems without disorder.

Figure 1

Amplitude of the $k\text{th}$ eigenvector at site $j$ for a chain with a quintuplet of closely spaced energies and $N=31$. The states of the quintuplet are basically localized on the two pairs of sites close to the ends of the chain.

Figure 2

Fidelity of transmission (6) of the Bell states $|{\psi }_1{\rangle }_{\pm }$ as a function of time for a chain with a quintuplet of closely spaced energies and $N=31$. Time is dimensionless, corresponding to the dimensionless energy spectra (2) and (4). The inset shows the region close to the perfect transfer time $t=\pi$.

Figure 3

Same as Fig. 2, for a chain with a quintuplet of closely spaced energies and $N=71$ and an additional contraction by $\Delta =60$.

Figure 4

Same as Fig. 1 for a chain with a quintuplet of closely spaced energies and $N=71$ and an additional contraction by $\Delta =60$. Seven states in the center of the energy spectrum are concentrated near the boundaries, whereas all other states extend through the whole system.

Figure 5

Same as Fig. 2 for a chain with a nonuplet of closely spaced energies and $N=321$.

Figure 6

Same as Fig. 3 for the Bell states $|{\psi }_2{\rangle }_{\pm }$.