Related papers: The space of density states in geometrical quantum…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense,…
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…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
We adopt the point of view that (Riemannian) classical and (loop-based) quantum descriptions of geometry are macro- and micro-descriptions in the usual statistical mechanical sense. This gives rise to the notion of geometrical entropy,…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
A relativistic framework for the description of bound states consisting of a large number of quantum constituents is presented, and applied to black-hole interiors. At the parton level, the constituent distribution, number and energy…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We analyze density profiles for atomic quantum Hall states, which are expected to form in systems of rotating cold atoms in the high-rotation limit. For a two-dimensional (single-layer) system we predict a density landscape showing plateaus…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
A quantum system can be entirely described by the K\"ahler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we…