Related papers: Kinematic approach to the mixed state geometric ph…
We cast observable measure of quantum coherence or asymmetry as a resource to control the quantum speed limit (QSL) for unitary evolutions. For non-unitary evolutions, QSL depends on that of the state of the system and environment together.…
The possibility of realization of quantum gates by means of the non-adiabatic geometric phase is considered. It is shown that the non-adiabatic phase can be used for quantum gates realization as well as the adiabatic one.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
The differential geometric aspects of Geometric Phases are reviewed.
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 phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
Correlation relations for the spin measurements on a pair of entangled particles scattered by the two separate arms of interferometers in hybrid setups of different types are investigated. Concurrence, entanglement of formation, quantum…
Generalized quantum measurements identifying non-orthogonal states without ambiguity often play an indispensable role in various quantum applications. For such unambiguous state discrimination scenario, we have a finite probability of…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We analyze the reduced density matrix for an arbitrary initial state of the composite system and compute the correction to the unitary…
Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…
Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly…
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…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate…
The effect of inter-subsystem coupling on the adiabaticity of composite systems and that of its subsystems is investigated. Similar to the adiabatic evolution defined for pure states, non-transitional evolution for mixed states is…
We consider a space with noncommutativity of coordinates and noncommutativity of momenta. It is shown that coordinates in noncommutative phase space depend on mass therefore they can not be considered as kinematic variables. Also,…
Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the…
The geometric phase due to the evolution of the Hamiltonian is a central concept in quantum physics, and may become advantageous for quantum technology. In non-cyclic evolutions, a proposition relates the geometric phase to the area bounded…
In this paper, we investigate the geometric phase of the field interacting with $\Xi $-type moving three-level atom. The results show that the atomic motion and the field-mode structure play important roles in the evolution of the system…