Related papers: Geometric phases in dressed state quantum computat…
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 introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
Motivated for the fault tolerant quantum computation, quantum gate by adiabatic geometric phase shift is extensively investigated. In this paper, we demonstrate the nonadiabatic scheme for the geometric phase shift and conditional geometric…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…
Geometric phases have been extensively investigated in a wide range of quantum systems, often revealing deep connections to the underlying topology of many-body states. In this work, we examine two geometric phases defined for mixed quantum…
Geometric quantization procedures go usually through an extension of the original theory (pre-quantization) and a subsequent reduction (selection of the physical states). In this context we describe a full geometrical mechanism which…
We establish a topological sum rule, $\nu_U = \frac{1}{2\pi}\sum_n\gamma_n = 2m\nu_H$, connecting the geometric phases accumulated by a two-qubit system over a complete basis of initial states to the winding number $\nu_H$ classifying its…
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…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
We analyze a new scheme for quantum information processing, with superconducting charge qubits coupled through a cavity mode, in which quantum manipulations are insensitive to the state of the cavity. We illustrate how to physically…
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the…
The differential geometric aspects of Geometric Phases are reviewed.
The form of the eigenstates of an atom coupled to a cavity mode displaying a three dimensional periodic profile are obtained. It is shown that the quantized motion leads to degenerate states where the atomic degrees of freedom are masked,…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
We study the geometric phase of an open two-level quantum system under the influence of a squeezed, thermal environment for both non-dissipative as well as dissipative system-environment interactions. In the non-dissipative case, squeezing…
Quantum mechanics is able to predict challenging behaviors even in the simplest physical scenarios. These behaviors are possible because of the important dynamical role that phase plays in the evolution of quantum systems, and are very…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…