  Information theory tells us that if the rate of sending information across a
noisy channel were above the capacity of that channel, then the transmission
would necessarily be unreliable. For classical information sent over classical
or quantum channels, one could, under certain conditions, make a stronger
statement that the reliability of the transmission shall decay exponentially to
zero with the number of channel uses and the proof of this statement typically
relies on a certain fundamental bound on the reliability of the transmission.
Such a statement or the bound has never been given for sending quantum
information. We give this bound and then use it to give the first example where
the reliability of sending quantum information at rates above the capacity
decays exponentially to zero. We also show that our framework can be used for
proving generalized bounds on the reliability.
