Lossless quantum data compression and variable-length coding

Abstract

In order to compress quantum messages without loss of information it is\nnecessary to allow the length of the encoded messages to vary. We develop a\ngeneral framework for variable-length quantum messages in close analogy to the\nclassical case and show that lossless compression is only possible if the\nmessage to be compressed is known to the sender. The lossless compression of an\nensemble of messages is bounded from below by its von-Neumann entropy. We show\nthat it is possible to reduce the number of qbits passing through a quantum\nchannel even below the von-Neumann entropy by adding a classical side-channel.\nWe give an explicit communication protocol that realizes lossless and\ninstantaneous quantum data compression and apply it to a simple example. This\nprotocol can be used for both online quantum communication and storage of\nquantum data.\n