Private capacity of quantum channels induced by nonstabilizer environmental states
Phys. Rev. A 114, 032432 – Published 14 September, 2026
DOI: https://doi.org/10.1103/hvzc-g31h
Abstract
We investigate the private capacity of quantum channels using the recently proposed quantum convolution theory for discrete-variable quantum systems. We focus on the role played by magic resources in this framework. First, for a broad class of convolutional channels, we find that the private capacity is zero if the fixed environmental state is a stabilizer state. Moreover, we show that the private capacity can be nonzero for some magic environmental states. For pure environmental states, we further prove that the private capacity of a discrete beam-splitter channel is upper bounded by twice the modified relative entropy of magic of the environment. In addition, if the environmental state exhibits a certain symmetric structure, even if it is magic, the corresponding private capacity will also vanish for a class of convolutional channels. Together, these results show that environmental magic is necessary but not sufficient for positive private capacity in the channel class considered here, while also providing a quantitative upper bound on the achievable private rate.
