Shannon theory beyond quantum: information content of a source
- URL: http://arxiv.org/abs/2112.12689v2
- Date: Tue, 5 Apr 2022 11:46:02 GMT
- Title: Shannon theory beyond quantum: information content of a source
- Authors: Paolo Perinotti, Alessandro Tosini, Leonardo Vaglini
- Abstract summary: We extend the definition of information content to operational probabilistic theories.
We prove relevant properties as the subadditivity, and the relation between purity and information content of a state.
- Score: 68.8204255655161
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The information content of a source is defined in terms of the minimum number
of bits needed to store the output of the source in a perfectly recoverable
way. A similar definition can be given in the case of quantum sources, with
qubits replacing bits. In the mentioned cases the information content can be
quantified through Shannon's and von Neumann's entropy, respectively. Here we
extend the definition of information content to operational probabilistic
theories, and prove relevant properties as the subadditivity, and the relation
between purity and information content of a state. We prove the consistency of
the present notion of information content when applied to the classical and the
quantum case. Finally, the relation with one of the notions of entropy that can
be introduced in general probabilistic theories, the maximum accessible
information, is given in terms of a lower bound.
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