Fighting noise with noise in realistic quantum teleportation

We investigate how the efficiency of the quantum teleportation protocol is affected when the qubits involved in the protocol are subjected to noise or decoherence. We study all types of noise usually encountered in real-world implementations of quantum communication protocols, namely, the bit-flip, phase-flip (phase damping), depolarizing, and amplitude-damping noise. Several realistic scenarios are studied in which a part or all of the qubits employed in the execution of the quantum teleportation protocol are subjected to the same or different types of noise. We find noise scenarios not yet known in which more noise or less entanglement lead to more efficiency. Furthermore, we show that if noise is unavoidable it is better to subject the qubits to different noise channels in order to obtain an increase in the efficiency of the protocol.

Figure 1

Efficiency of the teleportation protocol when only the input qubit is affected by a noisy environment, with $p_{{}_I}$ representing the probability for the noise to act on the qubit. The dashed line, $\langle \overline{F}\rangle =2/3$, marks the value below which classical protocols (no entanglement) give the same efficiency [23].

Figure 2

Efficiency of the teleportation protocol when both the input qubit $\left(p_{{}_I}\right)$ and Bob's qubit $\left(p_{{}_B}\right)$ are affected by a noisy environment. The dashed line, $\langle \overline{F}\rangle =2/3$, marks the value below which classical protocols (no entanglement) give the same efficiency [23]. Here the input qubit is always subjected to the bit-flip $\left(BF\right)$ noise while Bob's qubit may suffer from several types of noise.

Figure 3

Efficiency of the teleportation protocol when both the input qubit $\left(p_{{}_I}\right)$ and Bob's qubit $\left(p_{{}_B}\right)$ are affected by a noisy environment. The dashed line, $\langle \overline{F}\rangle =2/3$, marks the value below which classical protocols (no entanglement) give the same efficiency [23]. Here the input qubit is always subjected to the phase-flip $\left(PhF\right)$ noise while Bob's qubit may suffer from several types of noise.

Figure 4

Efficiency of the teleportation protocol when Alice's qubits suffer the bit-flip noise $\left(p_{{}_I}=p_{{}_A}=p\right)$ and Bob's qubits $\left(p_{{}_B}\right)$ are affected by several types of noise. The dashed line, $\langle \overline{F}\rangle =2/3$, marks the value below which classical protocols (no entanglement) give the same efficiency [23].

Figure 5

Efficiency of the teleportation protocol for different channels subjected to the same noise, namely, the amplitude-damping noise $\left(p_{{}_A}=p_{{}_B}=p\right)$, with the input qubit in a noiseless environment. The dashed line, $\langle \overline{F}\rangle =2/3$, marks the value below which classical protocols (no entanglement) give the same efficiency [23].

Figure 6

Efficiency of the teleportation protocol when both the input qubit $\left(p_{{}_I}\right)$ and Bob's qubit $\left(p_{{}_B}\right)$ are affected by a noisy environment. The dashed line, $\langle \overline{F}\rangle =2/3$, marks the value below which classical protocols (no entanglement) give the same efficiency [23]. Here the input qubit is always subjected to the depolarizing $\left(D\right)$ noise, while Bob's qubit may suffer from several types of noise.

Figure 7

Efficiency of the teleportation protocol when both the input qubit $\left(p_{{}_I}\right)$ and Bob's qubit $\left(p_{{}_B}\right)$ are affected by a noisy environment. The dashed line, $\langle \overline{F}\rangle =2/3$, marks the value below which classical protocols (no entanglement) give the same efficiency [23]. Here the input qubit is always subjected to the amplitude-damping $\left(AD\right)$ noise, while Bob's qubit may suffer from several types of noise.