相关论文: Characterization of symmetric monotone metrics on …
Morozova and Chentsov (Morozova and Chentsov 90) studied Riemannian metrics on the set of probability measures. They showed that, up to a constant factor, the Fisher information is the only Riemannian metric which is monotone under…
Chentsov studied Riemannian metrics on the set of probability measures from the point of view of decision theory. He proved that up to a constant factor the Fisher information is the only metric which is monotone under stochastic…
In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by…
The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions…
A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest. Using (complex projective) 2-designs, we construct measurements on a pair of…
An analytical approach is developed to the problem of computation of monotone Riemannian metrics (e.g. Bogoliubov-Kubo-Mori, Bures, Chernoff, etc.) on the set of quantum states. The obtained expressions originate from the Morozova, Chencov…
Information metrics give lower bounds for the estimation of parameters. The Cencov-Morozova-Petz Theorem classifies the monotone quantum Fisher metrics. The optimum bound for the quantum estimation problem is offered by the metric which is…
The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric…
We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…
The aim of the manuscript is to characterize monotone `metric' in the space of Markov map. Here, `metric' means the square of the norm defined on the tangent space, and not necessarily induced from an inner product (this property hereafter…
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all…
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 proposed in J. Math. Phys. v.57,071903 (2016) analytical expansion of monotone (contractive) Riemannian metrics (called also quantum Fisher information(s)) in terms of moments of the dynamical structure factor (DSF) relative to an…
The Quantum Fisher Information (QFI) is a geometric measure of state deformation calculated along the trajectory parameterizing an ensemble of quantum states. It serves as a key concept in quantum metrology, where it is linked to the…
Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, quantum metrology for non-Markovian…
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…
The aim of the manuscript is to characterize monotone metric in the space of Markov map. Here, metric may not be Riemanian, or equivalently, may not be induced from an inner product. So far, there have been plenty of literatures on the…
The theory of monotone Riemannian metrics on the state space of a quantum system was established by Denes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant - monotone - metric can be interpreted…
We prove that for a large class of quantum Fisher information, a quantum channel is sufficient for a family of quantum states, i.e., the input states can be recovered from the output, if and only if the quantum Fisher information is…
We define a mixed topology on the fiber space $\cup_\mu \oplus^n L^n(\mu)$ over the space $\mathcal{M}(\Omega)$ of all finite non-negative measures $\mu$ on a separable metric space $\Omega$ provided with Borel $\sigma$-algebra. We define a…