Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation

Characterization of several kinds of quantum analogues of relative entropy

Quantum relative entropy $D(ρ\|σ)\defeq\Tr ρ(\log ρ- \log σ)$ plays an important role in quantum information and related fields. However, there are many quantum analogues of relative entropy. In this paper, we characterize these analogues from information geometrical viewpoint. We also consider the naturalness of quantum relative entropy among these analogues.

The energy level crossing behavior and quantum Fisher information in a quantum well with spin-orbit coupling

We study the energy level crossing behavior in two-dimensional quantum well with the Rashba and Dresselhaus spin-orbit couplings (SOCs). By mapping the SOC Hamiltonian onto an anisotropic Rabi model, we obtain the approximate ground state and its quantum Fisher information (QFI) via performing a unitary transformation. We find that the energy level crossing can occur in the quantum well system within the available parameters rather than in cavity and circuit quantum eletrodynamics systems. Futhermore, the influence of two kinds of SOCs on the QFI is investigated and an intuitive explanation fr…

基于群体编码的海森堡标度

Heisenberg scaling based on population coding

针对Fisher信息无法反映全局结构的问题，提出以互信息作为群体编码视角下的替代品质因数，并证明若干酉模型可实现海森堡标度。

Net Fisher information measure versus ionization potential and dipole polarizability in atoms

The net Fisher information measure, defined as the product of position and momentum Fisher information measures and derived from the non-relativistic Hartree-Fock wave functions for atoms with Z=1-102, is found to correlate well with the inverse of the experimental ionization potential. Strong direct correlations of the net Fisher information are also reported for the static dipole polarizability of atoms with Z=1-88. The complexity measure, defined as the ratio of the net Onicescu information measure and net Fisher information, exhibits clearly marked regions corresponding to the periodicity …

Quantum and Fisher Information from the Husimi and Related Distributions

The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczyński (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262 [1996]). In the former work, a metric (the Monge one, specifically) over generalized Husimi distributions was employed to define a distance between two arbitrary density matrices. In the Petz-Sudar work (completing a program of Chentsov), the quantum analogue of the (classically unique) Fisher information (montone) metric of a probability simplex was extended to defi…

利用微扰方法研究四次势与对称势中的量子信息测度

Quantum Information Measures in Quartic and Symmetric Potentials using perturbative approach

本文用微扰法求解薛定谔方程，研究四次势与对称势阱中Shannon和Fisher信息随阱宽的变化，验证熵和不变性、Fisher信息行为及BBM不等式。