Related papers: A thermofield-double model of Uhlmann anholonomy
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 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…
Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum…
We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the…
A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrodinger evolution of a quantum system is a geodesic motion on the space of states of the system…
Studies have shown that the Hilbert spaces of non-Hermitian systems require nontrivial metrics. Here, we demonstrate how evolution dimensions, in addition to time, can emerge naturally from a geometric formalism. Specifically, in this…
Holonomic phases---geometric and topological---have long been an intriguing aspect of physics. They are ubiquitous, ranging from observations in particle physics to applications in fault tolerant quantum computing. However, their…
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…
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…
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…
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by…
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…
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…
A unifying framework for identifying distance and holonomy for decompositions of density operators is introduced. Parallelity between quantum ensembles is defined by minimizing this distance over allowed decompositions. The minimum is a…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
We study the behaviour of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyse some of the paradigmatic cases of topological insulators and superconductors in dimension one, as well as the…
We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of…
The nonadiabatic holonomic quantum computation based on the geometric phase is robust against the built-in noise and decoherence. In this work, we theoretically propose a scheme to realize nonadiabatic holonomic quantum gates in a surface…
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…