Related papers: The quantum geometric tensor from generating funct…
Recently, there has been considerable interest in the application of information geometry to quantum many body physics. This interest has been driven by three separate lines of research, which can all be understood as different facets of…
The generating function method that we had developing has various applications in physics and not only interress undergraduate students but also physicists. We solve simply difficult problems or unsolved commonly used in quantum, nuclear…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
A covariant - tensor method for $SU(2)_{q}$ is described. This tensor method is used to calculate q - deformed Clebsch - Gordan coefficients. The connection with covariant oscillators and irreducible tensor operators is established. This…
Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$ to extract a pre-symplectic form and a…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this…
A geometric framework for quantum statistical estimation is used to establish a series of higher order corrections to the Heisenberg uncertainty relations associated with pairs of canonically conjugate variables. These corrections can be…
Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the…
Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate…
The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry…
The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the…
We compute both analytically and numerically the geometry of the parameter space of the anharmonic oscillator employing the quantum metric tensor and its scalar curvature. A novel semiclassical treatment based on a Fourier decomposition…
We introduce a new methodology to characterize properties of quantum spacetime in a strongly quantum-fluctuating regime, using tools from topological data analysis. Starting from a microscopic quantum geometry, generated nonperturbatively…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda) and extremely…
We report the digital quantum simulation of a hamiltonian involved in the generation of quantum entanglement by gravitational means. In particular, we focus on a pair of quantum harmonic oscillators, whose interaction via a quantum…