Feedback in Quantum Communication

Communication is primarily the generation of correlations between two parties. The transmission of information is undertaken to correlate the received message with an possible set of transmitted messages. In the classical theory of information the maximum rate of information transmission through a memoryless channel is given by a measure of the maximum correlation that may be generated through the channel. The correlation measure is the mutual information between the sender’s alphabet and the receiver’s output alphabet. Utilizing feedback, where the receiver’s output state is communicated noiselessly to the sender cannot increase the maximum asymptotic rate of transmission. The capacity, defined as the maximum rate of information transfer per channel use, cannot then be increased by the use of feedback. Feedback in quantum information theory becomes a more slippery concept, mainly due to the quantum no-cloning theorem. The output state of the receiver cannot be copied with perfect fidelity, and so the natural generalisation of the classical feedback scenario cannot take place. A more subtle approach is then needed in both the definition and implications of feedback in quantum communication.