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<p>Methods of information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of homogeneous statistical manifolds. In particular we construct explicit examples of homogeneous statistical manifolds of low dimension. The second purpose is to classify 3-dimensional Lie groups admitting non-trivial conjugate-symmetric left-invariant statistical structure.</p>

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Homogeneous statistical manifolds

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Jun-ichi Inoguchi,
  • Yu Ohno

摘要

Methods of information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of homogeneous statistical manifolds. In particular we construct explicit examples of homogeneous statistical manifolds of low dimension. The second purpose is to classify 3-dimensional Lie groups admitting non-trivial conjugate-symmetric left-invariant statistical structure.