Information storing yields a point-asymmetry of state space in general probabilistic theories

Keiji Matsumoto, Gen Kimura

Research output: Contribution to journalArticlepeer-review

Abstract

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 [9] and [28] 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. Finally, as a technical byproduct, the existence of a Helstrom family for any probabilistic models is shown.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Feb 4

ASJC Scopus subject areas

  • General

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