Is it possible to MAC a quantum state with a classical key under reasonable assumption?
Howard Barnum, Claude Crepeau, Daniel Gottesman, Adam Smith, Alain Tapp. "Authentication of Quantum Messages", FOCS 2002.

http://www.cse.psu.edu/~ads22/pubs/PS-CSAIL/BCGST02-focs-final.pdf

As with encryption, there is a protocol that requires no computational assumptions. It uses a key of length about 2n+2k to authenticate n qubits with security level 2^{-k}.