Stefan Berens Conditional Rényi entropy
نویسندگان
چکیده
The introduction of the Rényi entropy allowed a generalization of the Shannon entropy and unified its notion with that of other entropies. However, so far there is no generally accepted conditional version of the Rényi entropy corresponding to the one of the Shannon entropy. Different definitions proposed so far in the literature lacked central and natural properties one way or another. In this thesis we propose a new definition for the conditional case of the Rényi entropy. Our new definition satisfies all of the properties we deem natural. First and foremost, it is consistent with the existing, commonly accepted, definition of the conditional Shannon entropy as well as with the right notion of the conditional min entropy. Furthermore, and in contrast to previously suggested definitions, it satisfies the two natural properties that are monotonicity and (weak) chain rule and which we feel need to be satisfied by any ‘good’ entropy notion. Another characteristic of our new definition is that it can be formulated in terms of the Rényi divergence. Additionally, it enables the use of (entropy) splitting. We conclude with an application where we use our new entropy notion as a tool to analyze a particular quantum cryptographic identification scheme.
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