A modified quantum teleportation protocol broadens the scope of the classical forbidden-interval theorems for stochastic resonance. The fidelity measures performance of quantum communication. The sender encodes the two classical bits for quantum teleportation as weak bipolar subthreshold signals and sends them over a noisy classical channel. Two forbidden-interval theorems provide a necessary and sufficient condition for the occurrence of the nonmonotone stochastic resonance effect in the fidelity of quantum teleportation. The condition is that the noise mean must fall outside a forbidden interval related to the detection threshold and signal value. An optimal amount of classical noise benefits quantum communication when the sender transmits weak signals, the receiver detects with a high threshold, and the noise mean lies outside the forbidden interval. Theorems and simulations demonstrate that both finite-variance and infinite-variance noise benefit the fidelity of quantum teleportation.
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