Determining whether a noisy quantum channel can be used to reliably transmit quantum information is a challenging problem in quantum information theory. This is because it requires computation of the channel’s coherent information for an unbounded number of copies of the channel.
A team of researchers has devised an elementary perturbative technique to solve this problem in a wide variety of circumstances. Their analysis reveals that a channel’s ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces.
They exploited this link to develop easy tests which can be used to detect positivity of quantum channel capacities simply by comparing the channels’ input, output, and environment dimensions. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of their method. Notably, in all these examples, the coherent information of a single copy of the channel turns out to be positive.
The paper has been published in npj Quantum Information.
