Consistency of the Shannon entropy in quantum experiments (12 pages)

Kenneth H. Norwich

PierGianLuca Porta Mana

The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analysed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.

S. A. Trigger, Jörn Dunkel

PierGianLuca Porta Mana

Brukner and Zeilinger [Phys. Rev. A 63 (2001) 022113] have claimed that two properties of the Shannon conditional entropy are violated in quantum experiments. It is shown here that the analysis by which they support their claim is flawed by the fact that they mix (probabilities and) entropies relative to different contexts, i.e., different experimental arrangements. It is also argued that the context-dependency of the Shannon entropy has nothing to do with the quantum or classical nature of experiments.

Nilanjana Datta

Oziel Ribeiro de Araújo, Lucas S. Marinho, H. A. S. Costa +2 more

The Shannon entropy has been used to study the localization/delocalization of a distribution for different systems. Greater increased localization was associated with the smaller values and increased delocalization with the larger values of the Shannon entropy. In this paper, we show that for the double-slit experiment in the position and momentum spaces, smaller values of the Shannon entropy are associated with larger number of interference fringes and larger values of the Shannon entropy with smaller number of interference fringes.