Related papers: Hermite-Gaussian model for quantum states
Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to…
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…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions (tomograms) is…
Quantum Fisher Information (QFI) is a fundamental quantity in quantum parameter estimation theory, characterizing the ultimate precision bound of parameter estimation. In this work, we investigate QFI for quantum states in non-Hermitian…
Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
This post is the author's doctoral dissertation back in 1997. The dissertation covers following four kinds of problems: First, it studies achievable Cramer-Rao type bounds of various multi-parameter pure state models. Second, it relates…
We apply a Gaussian state formalism to track fluctuating perturbations that act on the position and momentum quadrature variables of a harmonic oscillator. Following a seminal proposal by Tsang and Caves [Phys. Rev. Lett. 105, 123601…
Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled…
The logarithmic derivative (or, quantum score) of a positive definite density matrix appearing in the quantum Fisher information is discussed, and its exact expression is presented. Then, the problem of estimating the parameters in a class…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
The quantum geometric tensor (QGT) fundamentally encodes the geometry and topology of quantum states in both Hermitian and non-Hermitian regimes. While adiabatic perturbation theory links its real part (quantum metric) and imaginary part…
The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular…
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…
The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
Quantum parameter estimation with Hermitian systems has been applied in various fields, but there are relatively few results concerning non-Hermitian systems. Here, we study the quantum parameter estimation for general non-Hermitian…
Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…