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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. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both the two information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating-wave approximation. We further express the two information quantities in terms of the Bloch vector for a qudit, by expanding the density matrix and Hermitian operators in a common set of generators of the Lie algebra $mathfrak{su}(d)$. By calculating the dynamical quantum Fisher information, we find that the collisional dephasing significantly diminishes the precision of phase parameter with the Ramsey interferometry.
The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we analyze a
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lea
We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system to a set
It is well known that a suggestive relation exists that links Schrodingers equation (SE) to the information-optimizing principle based on Fishers information measure (FIM). The connection entails the existence of a Legendre transform structure underl
In the present article, we consistently develop the main issues of the Bloch vectors formalism for an arbitrary finite-dimensional quantum system. In the frame of this formalism, qudit states and their evolution in time, qudit observables and their e