Information storing yields a point-asymmetry of state space in general probabilistic theories. (arXiv:1802.01162v1 [quant-ph])

The state spaces of both classical and quantum systems have a point-asymmetry
about the maximally mixed state except for bit and qubit systems. In this
paper, we find an informational origin of this asymmetry: In any operationally
valid probabilistic model, the state space has a point-asymmetry in order to
store more than a single bit of information. In particular, we introduce a
storable information as a natural measure of the storability of information and
show the quantitative relation with the so-called Minkowski measure of the
state space, which is an affinely invariant measure for point-asymmetry of a
convex body. We also show the relation between these quantities and the
dimension of the model, inducing some known results in \cite{ref:KNI} and
\cite{ref:FMPT} as its corollaries. Also shown are a generalization of weaker
form of the dual structure of quantum state spaces, and a generalization of the
maximally mixed states as points of the critical set.

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