The Adaptive Classical Capacity of a Quantum Channel, or Information Capacities of Three Symmetric Pure States in Three Dimensions

Abstract

We investigate the capacity of three symmetric quantum states in three real dimensions to carry classical information. Several such capacities have already been defined, depending on what operations are allowed in the sending and receiving protocols. These include the C_{1,1} capacity, which is the capacity achievable if separate measurements must be used for each of the received states, and the C_{1,infinity} capacity, which is the capacity achievable if joint measurements are allowed on the tensor product of all the received states. We discover a new classical information capacity of quantum channels, the adaptive capacity C_{1,A}, which lies strictly between the C_{1,1} and the C_{1,infinity} capacities. The adaptive capacity requires each of the signals to be measured by a separate apparatus, but allows the quantum states of these signals to be measured in stages, with the first stage partially reducing their quantum states, and where measurements in subsequent stages which further reduce the quantum states may depend on the results of a classical computation taking as input the outcomes of the first round of measurements.