One classical bit perspective on the noisy teleportation of quantum coherence

Quantum teleportation of an unknown quantum state necessitates the transmission of two classical bits of information; however, when the quantum state is partially known, only a single classical bit is required for the teleportation of its quantum coherence. In this study, we explore the teleportation of quantum coherence through noisy channels utilizing merely one classical bit of information. Our findings reveal that, in contrast to noise-free scenarios, the generalized Bell states POVM (GBS-POVM) and non-maximally entangled states may surpass the performance of Bell states POVM (BS-POVM) and maximally entangled states in enabling probabilistic teleportation of quantum coherence. Nevertheless, when assessing the average amount of quantum coherence that can be teleported, maximally entangled states combined with BS-POVM emerges as the optimal choice, regardless of the type of noise encountered. Moreover, we uncover that for bit-phase-flip (BPF) noise, it is feasible to construct a suitable GBS-POVM that completely mitigates this noise. For other types of noise, we demonstrate that enhancing the teleportation of quantum coherence can be accomplished through entangling two consecutive uses of the same noisy channel, i.e., correlated noise. Notably, correlation effects arising from Pauli channels can entirely negate the detrimental impact of Pauli noises on the teleportation process for quantum coherence.