Related papers: On the geometric phase for Gaussian states
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 properties of the geometric phases between three quantum states are investigated in a high-dimensional Hilbert space using the Majorana representation of symmetric quantum states. We found that the geometric phases between the three…
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…
In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…
We demonstrate that a geometric phase, generated via a sequence of four optomechanical interactions, can be used to increase, or generate nonlinearities in the unitary evolution of a mechanical resonator. Interactions of this form lead to…
We describe a generalisation of the well known Pancharatnam geometric phase formula for two level systems, to evolution of a three-level system along a geodesic triangle in state space. This is achieved by using a recently developed…
Geometric Phase in Quantum Mechanics is generally formulated entirely in terms of geometric structure of the Complex Hilbert Space. We will exploit this fact in case of mixed states for three level open systems undergoing depolarization…
We compute the geometric phase for a spin-1/2 particle under the presence of a composite environment, composed of an external bath (modeled by an infinite set of harmonic oscillators) and another spin-1/2 particle. We consider both cases:…
We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
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…
The geometric phase associated with a many body ground state exhibits a signature of quantum phase transition. In this context, we have studied the behaviour of the geometric phase during a linear quench caused by a gradual turning off of…
We construct new invariants and give several theorems which determine in general (i) the number of physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings. We…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-N sequence of D Hermitian matrices X_\mu (\mu =1,2, ..., D) and construct a…
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles…
Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…
The manifold of ground states of a family of quantum Hamiltonians can be endowed with a quantum geometric tensor whose singularities signal quantum phase transitions and give a general way to define quantum phases. In this paper, we show…
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…