Quantum teleportation scheme by selecting one of multiple output ports

The scheme of quantum teleportation, where Bob has multiple $\left(N\right)$ output ports and obtains the teleported state by simply selecting one of the $N$ ports, is thoroughly studied. We consider both the deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state and (ii) the state is also optimized as well as Alice’s measurement. We analytically determine the optimal protocols for all the four cases and show the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of $N\to \infty$. The entanglement properties of the teleportation scheme are also discussed.

Figure 1

The setting of the teleportation scheme considered in this paper. Bob has multiple output ports and obtains the teleported state by simply selecting one of the $N$ ports according to the outcome $\left(i\right)$ of Alice’s measurement. To complete the teleportation, no unitary transformation to each output port is necessary because the state of one of the $N$ ports becomes the teleported state as it is.

Figure 2

The average fidelity $\left(f\right)$ in the deterministic scheme as a function of the number of output ports $\left(N\right)$. The asymptotic behavior $\left[1-1/\left(2N\right)\right]$ in the case of the maximally entangled $|\psi ⟩$ is also plotted by a dashed-dotted line.

Figure 3

The average success probability $\left(p\right)$ in the probabilistic scheme as a function of number of output ports $\left(N\right)$. The asymptotic behavior $\left[1-\sqrt{8/\left(\pi N\right)}\right]$ in the case of the maximally entangled $|\psi ⟩$ is also plotted by a dashed-dotted line.

Figure 4

The amount of entanglement as a function of the number of output ports $\left(N\right)$ in the probabilistic scheme. The initial amount of the optimal $|\psi ⟩$ (circles), the residual amount when the teleportation is successfully finished (rectangles), and the average residual amount (triangles) are plotted. The dotted line shows the eye guide that corresponds to the entanglement consumption by 1 ebit. The inset shows the same comparison of the initial and average residual amount up to $N=50$.