Private quantum codes: introduction and connection with higher rank   numerical ranges
  We give a brief introduction to private quantum codes, a basic notion in quantum cryptography and key distribution. Private code states are characterized by indistinguishability of their output states under the action of a quantum channel, and we show that higher rank numerical ranges can be used to describe them. We also show how this description arises naturally via conjugate channels and the bridge between quantum error correction and cryptography. 
D. W. Kribs and S. Plosker
math.OA quant-ph