Related papers: On the geometric phase for Gaussian states
We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled…
We show the explicit expression for the covariance matrix of general Gaussian states in terms of the symplectic group matrices. We discuss how the criteria to characterize squeezing and entanglement using the covariance matrix give rise to…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
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 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…
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…
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…
The geometric phase of a bi-particle model is discussed. For different initial states, especially when the initial state is pure or mixed, the geometric phase will show different properties. The relationship between the geometric phase and…
When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
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…
By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…
An explicit parameterization is given for the density matrices for $n$-state systems. The geometry of the space of pure and mixed states and the entropy of the $n$-state system is discussed. Geometric phases can arise in only specific…
Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak coupling limit…
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…
Gaussian states are the backbone of quantum information protocols with continuous variable systems, whose power relies fundamentally on the entanglement between the different modes. In the case of global pure states, knowledge of the…
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…
We analyze the geometric phase for an open quantum system when computed by resorting to a stochastic unravelling of the reduced density matrix (quantum jump approach or stochastic Schrodienger equations). We show that the resulting phase…
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 differential geometric aspects of Geometric Phases are reviewed.