  When sending quantum information over a channel, we want to ensure that the
message remains intact. Quantum error correction and quantum authentication
both aim to protect (quantum) information, but approach this task from two very
different directions: error-correcting codes protect against probabilistic
channel noise and are meant to be very robust against small errors, while
authentication codes prevent adversarial attacks and are designed to be very
sensitive against any error, including small ones.
  In practice, when sending an authenticated state over a noisy channel, one
would have to wrap it in an error-correcting code to counterbalance the
sensitivity of the underlying authentication scheme. We study the question of
whether this can be done more efficiently by combining the two functionalities
in a single code. To illustrate the potential of such a combination, we design
the threshold code, a modification of the trap authentication code which
preserves that code's authentication properties, but which is naturally robust
against depolarizing channel noise. We show that the threshold code needs
polylogarithmically fewer qubits to achieve the same level of security and
robustness, compared to the naive composition of the trap code with any
concatenated CSS code. We believe our analysis opens the door to combining more
general error-correction and authentication codes, which could improve the
practicality of the resulting scheme.
