Gregory A. L. White

We study quantum information transmission through noisy multi-time processes, modeled as quantum combs that capture temporal correlations across multiple time steps. We focus on communication tasks in which admissible recovery operations are used to simulate an identity channel in the presence of environmental action over multiple time steps. Within this framework, we define the capacity of a quantum comb as the maximal number of qubits that can be transmitted with a given error. We provideSDP-computable converse bounds on both the maximal rate and error exponent for arbitrary combs. In particular, we introduce multi-time non-signaling and positive partial transpose (PPT) codes and develop a multi-time analogue of the Rains bound. As an application, we analyze the simulation of a temporally correlated depolarizing channel. We also obtain multi-time analogues of hypothesis-testing quantities under restricted multi-time measurements and their associated entropic quantities, which we believe to be of independent interest.