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