  Establishing the strong converse theorem for a communication channel confirms
that the capacity of that channel, that is, the maximum achievable rate of
reliable information communication, is the ultimate limit of communication over
that channel. Indeed, the strong converse theorem for a channel states that
coding at a rate above the capacity of the channel results in the convergence
of the error to its maximum value 1 and that there is no trade-off between
communication rate and decoding error. Here we prove that the strong converse
theorem holds for the product-state capacity of quantum channels with ergodic
Markovian correlated memory.
