| I analyze quantum channels with two senders and a single receiver, used in a variety of ways for the simultaneous transmission of classical and quantum information. Suppose that two independent senders, Alice and Bob, have access to different parts of the input of an arbitrary quantum channel with a single receiver Charlie. By invoking existing coding theorems for single-user channels, I prove two theorems which partially characterize the rates at which Alice and Bob can simultaneously transmit independent classical and quantum information to Charlie. The first theorem offers a multi-letter characterization of the classical-quantum capacity region, which consists of the rates at which it is possible for Alice to send classical information while Bob sends quantum information. The second theorem gives a multi-letter characterization of the quantum-quantum capacity region, which is comprised of the rates at which Alice and Bob can each send quantum information. As an application, for each situation I introduce a channel for which the associated region is provably single-letter and describable via a simple analytic expression. Finally, I mention another characterization of the classical-classical region, concluding with a description of the full four-dimensional region of rates at which both senders can simultaneously send classical and quantum information. |
