Average fidelity and fidelity deviation in noisy quantum teleportation

TL;DR

This paper investigates the relationship between average fidelity and fidelity deviation in noisy quantum teleportation, revealing that maximum average fidelity guarantees perfect universality and proposing a machine-learning method to stabilize the process under noise.

Contribution

It establishes a fundamental link between fidelity and universality in quantum teleportation and introduces a machine-learning approach to mitigate noise effects.

Findings

Maximum average fidelity ensures zero fidelity deviation.

The relationship between F and D is tighter in the qubit case.

The proposed algorithm stabilizes teleportation fidelity under noise.

Abstract

We analyze the average fidelity (say, F) and the fidelity deviation (say, D) in noisy-channel quantum teleportation. Here, F represents how well teleportation is performed on average and D quantifies whether the teleportation is performed impartially on the given inputs, that is, the condition of universality. Our analysis results prove that the achievable maximum average fidelity ensures zero fidelity deviation, that is, perfect universality. This structural trait of teleportation is distinct from those of other limited-fidelity probabilistic quantum operations, for instance, universal-NOT or quantum cloning. This feature is confirmed again based on a tighter relationship between F and D in the qubit case. We then consider another realistic noise model where F decreases and D increases due to imperfect control. To alleviate such deterioration, we propose a machine-learning-based algorithm. We demonstrate by means of numerical simulations that the proposed algorithm can stabilize the system. Notably, the recovery process consists solely of the maximization of F, which reduces the control time, thus leading to a faster cure cycle.