Paolo Perinotti

The information content of a classical source is defined in terms of the number of bits per symbol that are needed to store the output of the source. An analogous definition is given for a quantum source, where the qubit replaces the bit. Here we show how to extend this definition to operational probabilistic theories. We also discuss some of its properties, such as subadditivity, and to what extent it can be interpreted as a measure of state purity. We also show that none of the proposed generalisations of entropy satisfies a generalised noiseless coding theorem, by means of a toy-theory, consisting of a bilocal version of standard classical theory.