Related papers: Operational geometric phase for mixed quantum stat…
We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that…
Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently…
Geometrical phases have been applied in virtually every major branch of physics and they play an important role in topology and knot theory in mathematics and quantum computation. However, most of the early works focus on pure quantum…
Geometric phase has been proposed as one of the promising methodologies to perform fault tolerant quantum computations. However, since decoherence plays a crucial role in such studies, understanding of mixed state geometric phase has become…
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…
Two geometric phases of mixed quantum states, known as the interferometric phase and Uhlmann phase, are generalizations of the Berry phase of pure states. After reviewing the two geometric phases and examining their parallel-transport…
Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for {\it mixed} input states. We report the first experiment to…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both non-degenerate as well as degenerate states. Starting with the non-degenerate case, we show that the usual procedure of…
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…
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…
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…
Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…
An adiabatic cyclic evolution of control parameters of a quantum system ends up with a holonomic operation on the system, determined entirely by the geometry in the parameter space. The operation is given either by a simple phase factor (a…
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…
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…
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…