Fidelity deviation in quantum teleportation

Abstract

We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel-we here consider the so-called Werner channel. To characterize our results, we introduce a two-dimensional space defined by the aforementioned measures, in which the performance of the teleportation is represented as a point with the channel noise parameter. Through further analysis, we specify some regions drawn for different channel conditions, establishing the connection to the dissimilar contributions of the entanglement to the teleportation and the Bell inequality violation.

Simplified Protocol of Quantum Teleportation

“…Therefore, we will need a good metrics to be able to evaluate said transfer quality. Then, we recommend here two versions of the most used metric in teleportation, the fidelity [25]. These versions have to do with the characteristic of the state to teleport, i.e., if it is pure or a mixed state…”

“…Fidelity f is a metric which gives us the closeness between an initial and final state in a quantum process [25]. It has widely been used to characterize the performance of various quantum information tasks.…”

“…It has widely been used to characterize the performance of various quantum information tasks. Fidelity f is bounded by 0 ≤ f ≤ 1, where the unit fidelity (f = 1) implies that the initial and final states are equivalent [25]. Quantum teleportation is designed to transmit all possible (unknown) input states, thus a measure of averaging over all inputs is used.…”

“…Thus, F shows the optimality of the quantum teleportation. There it is shown that the unit average fidelity (F = 1) can be obtained when the two remote parties share the maximally entangled states, whereas F = 2/3 is the maximally attainable one in any classical schemes which cannot use the entanglement [25]. …”

Simplified Protocol of Quantum Teleportation

“…Therefore, we will need a good metrics to be able to evaluate said transfer quality. Then, we recommend here two versions of the most used metric in teleportation, the fidelity [25]. These versions have to do with the characteristic of the state to teleport, i.e., if it is pure or a mixed state [25][26][27].…”