Shannon's information is not entropy

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Contrary to the widespread belief, Shannon's information and entropy are not in general equivalent. The purpose of this Letter is to discuss their conceptual difference and to pinpoint to mathematical reason for this. This fact is further illustrated through a toy model consisting of a harmonic oscillator in a coherent state, showing explicitly the dependence of Shannon's information on the class of quantum states the system is in. The interrelation between Shannon's information and entropy is reestablished after a theorem telling which class of states maximizes the (missing) information is proved. We shall conclude that entropy is the maximum amount of missing information.

Original languageEnglish
Pages (from-to)361-365
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number7-8
StatePublished - 15 Apr 1991
Externally publishedYes


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