Comment on " Conceptual Inadequacy of Shannon Information ... " by C. Brukner and A. Zeilinger I Interpretations of Shannon Entropy

It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular interpretation of Shannon’s H-function (related to consecutive measurements), and is shown explicitly to fail for other physical interpretations. Further, it is shown that Shannon and von Neumann entropies have in fact a common fundamental significance, connected to the existence of a unique geometric measure of uncertainty for classical and quantum ensembles. Some new properties of the “total information measure” proposed in quant-ph/0006087 are also given. I Interpretations of Shannon entropy Note that the term “Shannon entropy” will be used throughout for Shannon’s H function, rather than the term “Shannon information” used in [1], as the latter quantity in general involves a difference of entropies [2]. The main argument given in [1], against the use of Shannon entropy for quantum measurements, relies on showing that a particular interpretation of this quantity (involving consecutive measurements) does not accord with quantum mechanics. Here it is pointed out that an alternative interpretation may be given which does not involve consecutive measurements in any way. Hence no general conclusions on the adequacy of Shannon entropy can be drawn from the argument in [1]. Shannon showed that his H function could be derived from a set of axioms for “uncertainty” or “randomness” [3]. Numerous minor variations