Perfect teleportation with a partially entangled quantum channel

Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed by the sender (Alice), and classical information sent to the receiver (Bob) are three key ingredients in the procedure, which need to cooperate with each other. To study the relationship among the three parts, we propose a scheme for perfect teleportation of a qubit through a high-dimensional quantum channel in a pure state with two equal largest Schmidt coefficients. The scheme requires less entanglement of Alice's measurement but more classical bits than the original scheme via a Bell state. The two quantities increase with the entanglement of the quantum channel when its dimension is fixed and thereby can be regard as Alice's necessary capabilities to use the quantum channel. And the two capabilities appear complementary to each other.

Figure 1

Entanglement of Alice's measurement vs entanglement of quantum channels. Dashed curves show the values for case I, and solid ones show values for case II, accompanied by 10 000 random quantum channels with for each value of $n$: (a) $n=2$, (b) $n=4$, and (c) $n=6$. The results for $n=2$ overlap a single line.

Figure 2

Classical bits sent to Bob vs entanglement of quantum channels with the same parameters as Fig. 1.

Figure 3

The responses of fidelities to the random phases vs $a_0^2$. The dashed and dot-dashed curves show $f_0$ and $f_1$ in (30), respectively, and the solid line is for the value of $1/3$.