  We introduce and explicitly construct a quantum code we coin a "Pauli
Manipulation Detection" code (or PMD), which detects every Pauli error with
high probability. We apply them to construct the first near-optimal codes for
two tasks in quantum communication over adversarial channels. Our main
application is an approximate quantum code over qubits which can efficiently
correct from a number of (worst-case) erasure errors approaching the quantum
Singleton bound. Our construction is based on the composition of a PMD code
with a stabilizer code which is list-decodable from erasures.
  Our second application is a quantum authentication code for "qubit-wise"
channels, which does not require a secret key. Remarkably, this gives an
example of a task in quantum communication which is provably impossible
classically. Our construction is based on a combination of PMD codes,
stabilizer codes, and classical non-malleable codes (Dziembowski et al., 2009),
and achieves "minimal redundancy" (rate $1-o(1)$).
