相关论文: From quasi-entropy to skew information

For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…

This paper provides a mathematical framework for Fisher information analysis for inverse problems based on Gaussian noise on infinite-dimensional Hilbert space. The covariance operator for the Gaussian noise is assumed to be trace class,…

We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…

We revisit and improve joint concavity/convexity and monotonicity properties of quasi-entropies due to Petz in a new fashion. Then we characterize equality cases in the monotonicity inequalities (the data-processing inequalities) of…

We take the paradigm of interacting spin chains, the Heisenberg spin-$\frac{1}{2}$ XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An…

Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…

The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…

The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…

The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…

The dynamics of two variants of quantum Fisher information under decoherence are investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector.…

In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual…

We derive the quantum Fisher information for entropy estimation in a Gibbs state and show that it equals the inverse of the heat capacity, which is dual to the temperature Fisher information given by the heat capacity divided by the square…

We prove number of quantitative stability bounds for the cases of equality in Petz's monotonicity theorem for quasi-relative entropies defined in terms of an operator monotone decreasing functions. Included in our results is a bound in…

Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…

The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum uncertainty and classical uncertainty. By means of the skew information and the…

Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate…

In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…

Random matrix ensembles (RME) of quantal statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), had been applied in literature in study of following quantal…

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…

We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…