相关论文: Classical and quantum info-manifolds
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
This paper reviews Holevo's contributions to quantum information theory during the 20 century. At that time, he mainly studied three topics, classical-quantum channel coding, quantum estimation with Cramero-Rao approach, and quantum…
We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian. We provide the manifold with a flat connection,…
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum…
Here we describe the quantum limit to measurement of the classical gravitational field. Specifically, we write down the optimal quantum Cramer-Rao lower bound, for any single parameter describing a metric for spacetime. The standard…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
The free Fock space with corresponding - information creation and anihilation operators - supplies a kind of extended language in which equations for n-point information (n-pi) of classical and quantum physics are described. In this…
In this article a notion of information is presented which stresses the contextuality of quantum objects and their measurement. Mathematically this is reached by a quantification of the quantum mechanical surplus knowledge which has been…
When discussing the black hole information problem the term ``information flow'' is frequently used in a rather loose fashion. In this article I attempt to make this notion more concrete. I consider a Hilbert space which is constructed as a…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
We discuss the fundamental theoretical framework together with numerous results obtained by the authors and colleagues over an extended period of investigation on the Information Geometric Approach to Chaos (IGAC).
Assuming the minimal time to send a bit of information in the Einstein clock synchronization of the two clocks located at different positions, we introduce the extended metric to the information space. This modification of relativity…
We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain…
Information theory has its particles, bits and qubits, just as physics has electrons and photons. However, in physics we have a special category of objects with no clear counterparts in information theory: quasiparticles. They are…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
In the last decades, it has been understood that a wide variety of phenomena in quantum field theory (QFT) can be characterised using quantum information measures, such as the entanglement entropy of a state and the relative entropy between…
This paper introduces a new inequality in algorithmic information theory that can be seen as an extended coding theorem. This inequality has applications in new bounds between quantum complexity measures.