Transfer of different types of optical qubits over a lossy environment

We compare three different types of optical qubits for information transfer via quantum teleportation and direction transmission under photon losses. The three types of qubits are (1) qubits using the vacuum and the single-photon (VSP) states, (2) single-photon qubits using polarization degrees of freedom, i.e., polarized single-photon (PSP) qubits, and (3) coherent-state qubits that use two coherent states with opposite phases as the qubit basis. Our analysis shows that the teleportation scheme outperforms the direct transmission for most of cases as far as fidelities are concerned. Overall, VSP qubits are found to be the most efficient for both the direct transmission and teleportation under photon loss effects. The coherent-state qubits are more robust than PSP qubits either when their amplitudes are small as $\left|\alpha \right|\lesssim 1.22$ or when photon loss effects are strong. Our results would provide useful and timely information for the development of practical optical quantum information processing particularly in the context of hybrid architectures.

Figure 1

Schematics of two different ways to transfer qubits, i.e., (a) direct transmission and (b) quantum teleportation. The state $|\psi \rangle$ represents the unknown input state, and ${\rho }^D$ and ${\rho }^T$ represent the transferred states by means of each information transfer scheme, respectively.

Figure 2

Average fidelities of teleportation and direct transmission for (a) VSP qubits ($F_{\mathrm{V}}$) and (b) PSP qubits ($F_{\mathrm{P}}$) against the normalized time $r$. The solid curves represent the average fidelities for teleportation and the dashed curves correspond to those of the direct transmission. The horizontal dotted line indicates classical limit, $2/3$, which can be achieved by using a separable teleportation channel.

Figure 3

(a)–(c) Average fidelities $F_{\mathrm{C}}$ of teleportation (solid curve) and direct transmission (dashed curve) for coherent-state qubits with amplitudes (a) $\left|\alpha \right|=0.6$, (b) $\left|\alpha \right|\simeq 0.979$, and (c) $\left|\alpha \right|=1.5$ against the normalized time $r$. The horizontal dotted lines indicate the classical limit, 2/3. (d) The shaded area indicates the region where the teleportation outperforms the direct transmission. The time boundary between the teleportation-efficient and direct-transmission-efficient regions is indicated by $r_c$.

Figure 4

The upper figures show the average fidelities for (a) direct transmission and (b) quantum teleportation against the normalized time $r$. The solid and dashed curves represent the VSP and PSP qubits, respectively. The dot-dashed curve corresponds to the coherent-state qubits with $\left|\alpha \right|\simeq 0.979$, and the double-dot-dashed curve to the coherent-state qubits with $\left|\alpha \right|=3$. The shaded area is for the coherent-state qubits with $0\le \left|\alpha \right|\le 3$. The lower figures compare PSP and coherent-states qubits. The coherent-state qubits outperform PSP qubits in the dark-shaded regions while PSP qubits work better in the light-shaded regions for (c) direct transmission and (d) teleportation. In the unshaded regions of panels (c) and (d), both the fidelities are smaller than the classical bound $2/3$.