Related papers: A General Setting for Geometric Phase of Mixed Sta…
In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also…
Geometric phases play a fundamental role in understanding quantum topology, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
We calculate the geometric phase for an open system (spin-boson model) which interacts with an environment (ohmic or nonohmic) at arbitrary temperature. However there have been many assumptions about the time scale at which the geometric…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
A new definition and interpretation of geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected Principal Fibre Bundles, and the…
Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly…
A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the…
We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution,…
Off-diagonal mixed state phases based upon a concept of orthogonality adapted to unitary evolution and a proper normalisation condition are introduced. Some particular instances are analysed and parallel transport leading to the…
Entanglement properties of purified quantum states are of key interest for two reasons. First, in quantum information theory, minimally entangled purified states define the Entanglement of Purification as a fundamental measure for the…
We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of…
We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the…
Uhlmann's concept of quantum holonomy for paths of density operators is generalised to the off-diagonal case providing insight into the geometry of state space when the Uhlmann holonomy is undefined. Comparison with previous off-diagonal…
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…
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection…