Related papers: Geometric Phase using Diagonal Coherent State Repr…
The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are…
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…
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…
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…
Phase operators are constructed using a Klauder-Berezin coherent state quantization in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables phase leads…
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized…
On certain manifolds, the phase which appears in the scalar product of two coherent state vectors is twice the symplectic area of the geodesic triangle determined by the corresponding points on the manifold and the origin of the system of…
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…
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…
We calculate the geometric phase for an open system (spin-boson model) which interacts with an environment (ohmic or nonohmic) at arbitrary temperature. However there have been many assumptions about the time scale at which the geometric…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
This study explores the specific structure of 1D SPT phases with $G\times H$ symmetry ($G, H$ are finite non-Abelian groups) and constructs an order parameter. We demonstrate that this order parameter can comprehensively describe this…
We investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two…
We propose novel coherent-state phase concentration by probabilistic measurement-induced ampli- fication. The amplification scheme uses novel architecture, thermal noise addition (instead of single photon addition) followed by feasible…
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,…
Quantum technologies, encompassing communication, computation, and metrology, rely on the generation and control of non-Gaussian states of light. These states enable secure quantum communication, fault-tolerant quantum computation, and…
We investigate coherence in one- and two-photon optical systems, both theoretically and experimentally. In the first case, we develop the density operator representing a single photon state subjected to a non-dissipative coupling between…
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…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties…