11 - Quantum steganography

Abstract

Quantum steganography is the art of secretly transmitting quantum information while disguising the fact that any secret communication is taking place. Like classical steganography, this involves embedding the hidden communication within a seemingly innocent “covertext,” which in the quantum case is a quantum state. The best-developed protocol for quantum steganography uses an innocent cover state encoded in a quantum error-correcting code and transmitted over a quantum channel. The sender (Alice) hides a quantum state, a string of M quantum bits (qubits), in the N-qubit codeword by disguising the message as channel noise in such a way that the resulting state is indistinguishable from the innocent state with typical errors from the channel. The receiver (Bob) is able to decode the secret state. In general, quantum steganography requires Alice and Bob to share a secret key in advance, either as a string of random bits or a string of entangled qubit pairs (ebits). If the eavesdropper (Eve) has imperfect knowledge of the channel—perhaps because Alice and Bob have been systematically making it seem noisier than it really is—then Alice and Bob can communicate steganographically at a nonzero asymptotic rate. If Eve has exact knowledge of the channel, then Alice and Bob can still communicate secretly, but only sublinearly in the number of channel uses. This chapter reviews the basic quantum steganography protocol, describes different encoding methods, and proves bounds on the asymptotic rate of quantum steganographic communication and the rate of secret key consumption.