Related papers: Remarks on geometry and the quantum potential
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
Geometric and topological bounds are obtained for the first energy level gap of a particle constrained to move on a compact surface in 3-space. Moreover, geometric properties are found which allows for stationary and uniformly distributed…
In this paper we attempt to consider quantum superpositions from the perspective of the logos categorical approach presented in [26]. We will argue that our approach allows us not only to better visualize the structural features of quantum…
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. These pertain to a…
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
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…
In this paper, we review some features of quantum annealing and related topics from viewpoints of statistical physics, condensed matter physics, and computational physics. We can obtain a better solution of optimization problems in many…
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish…