  We derive one-shot upper bounds for quantum noisy channel codes. We do so by
regarding a channel code as a bipartite operation with an encoder belonging to
the sender and a decoder belonging to the receiver, and imposing constraints on
the bipartite operation. We investigate the power of codes whose bipartite
operation is non-signalling from Alice to Bob, positive-partial transpose (PPT)
preserving, or both, and derive a simple semidefinite program for the
achievable entanglement fidelity. Using the semidefinite program, we show that
the non-signalling assisted quantum capacity for memoryless channels is equal
to the entanglement-assisted capacity. We also relate our PPT-preserving codes
and the PPT-preserving entanglement distillation protocols studied by Rains.
Applying these results to a concrete example, the 3-dimensional Werner-Holevo
channel, we find that codes that are non-signalling and PPT-preserving can be
strictly less powerful than codes satisfying either one of the constraints, and
therefore provide a tighter bound for unassisted codes. Furthermore,
PPT-preserving non-signalling codes can send one qubit perfectly over two uses
of the channel, which has no quantum capacity. We discuss whether this can be
interpreted as a form of superactivation of quantum capacity.
