Hiding Quantum Information in the Perfect Code

Center for Quantum Information Science and Technology,University of Southern California, Los Angeles, California 90089, USA(Dated: July 7, 2010; Received July 7, 2010; Revised; Accepted; Published)We present and analyze a protocol for quantum steganography where the sender (Alice) encodesher steganographic information into the error syndromes of the perfect (five-qubit) quantum error-correcting code, and sends it to the receiver (Bob) over a depolarizing channel. Alice and Bobshare a classical secret key, and hide quantum information in such a way that to an eavesdropper(Eve) without access to the secret key, the quantum message looks like an innocent codeword witha typical sequence of quantum errors. We calculate the average rate of key consumption, and showhow the protocol improves in performance as information is spread over multiple codeword blocks.Alice and Bob utilize different encodings to optimize the average number of steganographic bits thatthey can send to each other while matching the error statistics of the depolarizing channel.