  Using unreliable or noisy components for reliable communication requires
error correction. But which noise processes can support information
transmission, and which are too destructive? For classical systems any channel
whose output depends on its input has the capacity for communication, but the
situation is substantially more complicated in the quantum setting. We find a
generic test for incapacity based on any suitable forbidden transformation---a
protocol for communication with a channel passing our test would also allow us
to implement the associated forbidden transformation. Our approach includes
both known quantum incapacity tests---positive partial transposition (PPT) and
antidegradability (no cloning)---as special cases, putting them both on the
same footing. We also find a physical principle explaining the
nondistillability of PPT states: Any protocol for distilling entanglement from
such a state would also give a protocol for implementing the forbidden
time-reversal operation.
