  We derive upper bounds on the rate of transmission of classical information
over quantum channels by block codes with a given blocklength and error
probability, for both entanglement-assisted and unassisted codes, in terms of a
unifying framework of quantum hypothesis testing with restricted measurements.
Our bounds do not depend on any special property of the channel (such as
memorylessness) and generalise both a classical converse of Polyanskiy, Poor,
and Verd\'{u} as well as a quantum converse of Renner and Wang, and have a
number of desirable properties. In particular our bound on
entanglement-assisted codes is a semidefinite program and for memoryless
channels its large blocklength limit is the well known formula for
entanglement-assisted capacity due to Bennett, Shor, Smolin and Thapliyal.
