Related papers: A geometric framework for mixed quantum states bas…

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…

We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement…

Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann…

We consider and resolve the gap problem for almost quaternion-Hermitian structures, i.e. we determine the maximal and submaximal symmetry dimensions, both for Lie algebras and Lie groups, in the class of almost quaternion-Hermitian…

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.

Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation…

In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…

Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…

We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on the projective Hilbert space, we penalize covariant…

In this paper we study the para-hyperK\"ahler geometry of the deformation space of MGHC anti-de Sitter structures on $\Sigma\times\mathbb R$, for $\Sigma$ a closed oriented surface. We show that a neutral pseudo-Riemannian metric and three…

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states…

Lie algebroids provide a natural medium to discuss classical systems, however, quantum systems have not been considered. In aim of this paper is to attempt to rectify this situation. Lie algebroids are reviewed and their use in classical…

Let $(\acute{N},g,\nabla )$\ be a $2n$-dimensional quasi-statistical manifold that admits a pseudo-Riemannian metric $g$ (or $h)$ and a linear connection $\nabla $ with torsion. This paper aims to study an almost Hermitian structure $(g,L)$…

The structure of nearly K\"ahler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly K\"ahler manifold is…

We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…

On $4$-symmetric symplectic spaces, invariant almost complex structures -- up to sign -- arise in pairs. We exhibit some $4$-symmetric symplectic spaces, with a pair of "natural" compatible (usually not positive) invariant almost complex…

In this paper, we systematically establish the mathematical foundation for the $\text{U}^N(1)$ quantum geometric tensor (QGT) of mixed states Explicitly, we present a description based on the $\text{U}^N(1)$ principal bundle and derive a…

This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum…

Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…