Related papers: Uhlmann's geometric phase in presence of isotropic…
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…
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…
The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state…
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…
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…
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…
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…
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…
We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin-$\frac 1 2$ particles with a magnetic field acting on one of them. Within a depolarizing channel setup, an exact analytical…
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…
We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy…
Dynamic quantum phase transitions (DQPT) following quantum quenches exhibit singular behavior of the overlap between the initial and evolved states. Here we present a formalism to incorporate a geometric phase into quench dynamics of mixed…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are…
It is shown that Uhlmann's parallel transport of purifications along a path of mixed states represented by $2\times 2$ density matrices is just the path ordered product of Thomas rotations. These rotations are invariant under hyperbolic…
We consider arbitrary mixed state in unitary evolution and provide a comprehensive description of corresponding geometric phase in which two different points of view prevailing currently can be unified. Introducing an ancillary system and…
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…
We accept the implicit challenge of A. Uhlmann in his 1994 paper, "Parallel Lifts and Holonomy along Density Operators: Computable Examples Using O(3)-Orbits," by, in fact, computing the holonomy invariants for rotations of certain n-level…
In our investigation into the effects of the degree of polarization in modulation of partially polarized light we assume general settings of the interferometry of partially polarized lightwaves and perform theoretical analysis of the…
We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase…