Exact solutions for the fundamental limits of bosonic dephasing channels

Dephasing is a prominent noise mechanism that afflicts quantum information carriers, and it is one of the main challenges towards realizing useful quantum computation, communication, and sensing. In the case of bosonic systems, central to many applications, bosonic dephasing channels (BDCs) form a key class of non-Gaussian channels modeling noise affecting superconducting circuits or fiber-optic communication channels. Here we consider communication, discrimination, and estimation of BDCs, when using general strategies for these tasks as allowed by quantum mechanics. We provide an exact formula for the quantum, private, two-way assisted quantum, and secret-key agreement capacities of all BDCs, proving that that they are all equal to the relative entropy of the distribution underlying the channel to the uniform distribution. For discrimination and estimation tasks, we reduce difficult quantum problems to simple classical ones based on the probability densities defining the BDCs. We present upper bounds on the performance of various distinguishability and estimation tasks and show that they are also achievable. To the best of our knowledge, this is the first example of a non-Gaussian bosonic channel for which there are exact solutions for all of these tasks. Joint work with Zixin Huang (Macquarie University) and Ludovico Lami (University of Amsterdam).