Inferring channel memory, phase, and noise symmetry from the output of noisy quantum teleportation

Abstract We consider quantum teleportation channels in which a phase $$\\varphi$$ is imprinted onto the initial shared resource channel. The resource qudits interact with either two independent local environments or a common environment; we classify the noise as symmetric when the noise parameters on the two qudits are identical, and as asymmetric otherwise. By teleporting an arbitrary input state, we compute the Hilbert–Schmidt speed (HSS) and quantum Fisher information (QFI) of both the noisy resource channel and the teleported output state, each computed with respect to the initially encoded phase $$\\varphi$$ . We show that under symmetric noise, the HSS and QFI of the teleported output reproduce the same qualitative temporal behavior as their resource-channel counterparts. Because HSS can witness essential non-Markovianity—defined here as the violation of P-divisibility—within established contractivity regimes, this correspondence enables indirect inference of the resource channel’s memory effects from the output alone, without requiring direct access to the channel after teleportation. The output HSS and QFI also carry information about the initial phase, allowing its estimation. We further find that asymmetric noise can cause the qualitative dynamics of the output HSS and QFI to deviate from those of the resource channel. Such a deviation provides a diagnostic signature of environmental asymmetry. HSS can be evaluated without diagonalizing the density matrix, making it practical for high-dimensional qudit teleportation; moreover, the output state has a lower dimension than the bipartite resource channel, offering a lower-dimensional probe that substantially reduces measurement and computational overhead. Within the representative noise models studied, these findings establish a unified framework for extracting information about channel memory, phase sensitivity, and noise symmetry directly from the accessible teleported output.