Related papers: The Bloch vectors formalism for a finite-dimension…
The Bloch sphere is a familiar and useful geometrical picture of the dynamics of a single spin or two-level system's quantum evolution. The analogous geometrical picture for three-level systems is presented, with several applications. The…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
We present a comparative analysis of two different constructions of optimal-speed quantum Hamiltonian evolutions on the Bloch sphere. In the first approach (Mostafazadeh's approach), the evolution is specified by a traceless stationary…
Quantum fluctuations are fundamental in quantum technologies, affecting computing, sensing, cryptography, and thermodynamics. These include fluctuations in the variation of energy, charge, and other observables driven by interactions with…
A two-sphere ("Bloch" or "Poincare") is familiar for describing the dynamics of a spin-1/2 particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2) through an iterative procedure that constructs…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
We investigate monogamy of correlations and entropy inequalities in the Bloch representation. Here, both can be understood as direct relations between different correlation tensor elements and thus appear intimately related. To that end we…
We demonstrate that among all quantum teleportation protocols giving rise to the same average fidelity, those with aligned Bloch vectors between input and output states exhibit the minimum average trace distance. This defines optimal…
In this paper we review some known results on the motion of Bloch Oscillators in the crystal momentum representation. We emphasize that the acceleration theorem, as usually stated by most of the authors, is incomplete, but in the case of…
We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…
The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based…
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedman-Robertson-Walker model coupled to a massless scalar…
The problem of finding a vacuum definition for a single quantum field in curved space-times is discussed under a new geometrical perspective. The phase space dynamics of the quantum field modes are mapped to curves in a 2-dimensional…
The Bloch equation is the fundamental dynamical model applicable to arbitrary two-level systems. Analytical solutions to date are incomplete for a number of reasons that motivate further investigation. The solution obtained here for the…
In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the…
Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics.…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…
We discuss the structure of covariant equations, relating analytical properties of solutions to algebraic properties of the corresponding differential operator, specifically of its principal symbol. The principal symbol and its globality is…
We present the quantum model of the asymptotic dynamics underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario. The symmetry of the physical phase space enables making use of the affine coherent states quantization. Our results show…