Quantum Data Compression with Commuting Density Operators

A quantum source is a device that emits a sequence of quantum states. We consider the problem of compressing strings of these states when their density operators commute. These are two versions of the problem. In the visible case each term of the string is available to the encoder and in the blind or hissen case only the density operator of the string is available. but not the individual terms of the string. Both cases have been reformulated as classical informational-theoretic problems, and we solve these problems. Our analysis includes the scenario in which the decoder's reconstruction is imperfect.