Lossless quantum data compression and variable-length coding

摘要

In order to compress quantum messages without loss of information it isnecessary to allow the length of the encoded messages to vary. We develop ageneral framework for variable-length quantum messages in close analogy to theclassical case and show that lossless compression is only possible if themessage to be compressed is known to the sender. The lossless compression of anensemble of messages is bounded from below by its von-Neumann entropy. We showthat it is possible to reduce the number of qbits passing through a quantumchannel even below the von-Neumann entropy by adding a classical side-channel.We give an explicit communication protocol that realizes lossless andinstantaneous quantum data compression and apply it to a simple example. Thisprotocol can be used for both online quantum communication and storage ofquantum data.