Unification and Extension of Classic Information Principles

• URL: http://arxiv.org/abs/2207.07577v5
• Date: Mon, 12 Dec 2022 11:02:46 GMT
• Title: Unification and Extension of Classic Information Principles
• Authors: Jianfeng Xu
• Abstract summary: The sextuple model of the objective information theory (OIT) is a sufficient and necessary condition for discussing information with four basic postulations. The OIT is a novel information theory that can unify a variety of classical information principles and even accurately reveal the quantitative relationship between information, matter and energy.
• Score: 2.210780502414563
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To formulate a universal framework of information theory is beneficial. This study proves that the sextuple model of the objective information theory (OIT) is a sufficient and necessary condition for discussing information with four basic postulations. It is demonstrated for each metric defined in the OIT, there is a corresponding example in classical information theories or commonly used principles. Furthermore, atomic information is defined as the indivisible elementary information and the volume additivity is proven for combinations of atomic information. Consequently, the information volume that a single quantum carrier can carry is derived and a theorem relating information volume to mass, energy, and time is proved. All these efforts illustrate that the OIT is a novel information theory that can unify a variety of classical information principles and even accurately reveal the quantitative relationship between information, matter and energy.

Related papers

• The Generalized Capacity of a Quantum Channel [4.3512163406552]
  The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum information, the rate of the quantum capacity problem is expressed in terms of the coherent information. We define a transmission task, which includes as specific instances both classical information and quantum information capacity problems, and show that the transmission capacity of this task is characterized by the generalized information.
  arXiv  Detail & Related papers  (2023-09-25T13:52:19Z)
• Derivation of Standard Quantum Theory via State Discrimination [53.64687146666141]
  General Probabilistic Theories (GPTs) is a new information theoretical approach to single out standard quantum theory. We focus on the bound of the performance for an information task called state discrimination in general models. We characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.
  arXiv  Detail & Related papers  (2023-07-21T00:02:11Z)
• On the Joint Interaction of Models, Data, and Features [82.60073661644435]
  We introduce a new tool, the interaction tensor, for empirically analyzing the interaction between data and model through features. Based on these observations, we propose a conceptual framework for feature learning. Under this framework, the expected accuracy for a single hypothesis and agreement for a pair of hypotheses can both be derived in closed-form.
  arXiv  Detail & Related papers  (2023-06-07T21:35:26Z)
• Atomic and Subgraph-aware Bilateral Aggregation for Molecular Representation Learning [57.670845619155195]
  We introduce a new model for molecular representation learning called the Atomic and Subgraph-aware Bilateral Aggregation (ASBA) ASBA addresses the limitations of previous atom-wise and subgraph-wise models by incorporating both types of information. Our method offers a more comprehensive way to learn representations for molecular property prediction and has broad potential in drug and material discovery applications.
  arXiv  Detail & Related papers  (2023-05-22T00:56:00Z)
• Gacs-Korner Common Information Variational Autoencoder [102.89011295243334]
  We propose a notion of common information that allows one to quantify and separate the information that is shared between two random variables. We demonstrate that our formulation allows us to learn semantically meaningful common and unique factors of variation even on high-dimensional data such as images and videos.
  arXiv  Detail & Related papers  (2022-05-24T17:47:26Z)
• Shannon theory beyond quantum: information content of a source [68.8204255655161]
  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.
  arXiv  Detail & Related papers  (2021-12-23T16:36:06Z)
• Tracing Information Flow from Open Quantum Systems [52.77024349608834]
  We use photons in a waveguide array to implement a quantum simulation of the coupling of a qubit with a low-dimensional discrete environment. Using the trace distance between quantum states as a measure of information, we analyze different types of information transfer.
  arXiv  Detail & Related papers  (2021-03-22T16:38:31Z)
• Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics [0.0]
  It has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. Main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it.
  arXiv  Detail & Related papers  (2020-07-20T09:50:27Z)
• The Mathematical Structure of Integrated Information Theory [0.0]
  Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state.
  arXiv  Detail & Related papers  (2020-02-18T15:44:02Z)
• Integrated Information in Process Theories [0.0]
  We show how the key notions of Tononi et al.'s Integrated Information Theory can be studied within the simple graphical language of process theories. This allows IIT to be generalised to a broad range of physical theories, including as a special case the Quantum IIT of Zanardi, Tomka and Venuti.
  arXiv  Detail & Related papers  (2020-02-18T15:44:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.