Related papers: The Quantum Geometric Phase between Orthogonal Sta…
The state of a quantum system acquires a phase factor, called the geometric phase, when taken around a closed trajectory in the parameter space, which depends only on the geometry of the parameter space. Due to its sensitive nature, the…
A periodic perturbation such as a laser field cannot induce transitions between two decoupled states for which the transition matrix element vanishes. We show, however, that if in addition some system parameters are varied adiabatically,…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
The Pancharatnam phase deficit is defined as the difference between the Pancharat- nam phase acquired by the global system and the sum of the Pancharatnam phases acquired by subsystems during local unitary evolutions. We show that a…
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…
In the standard geometric approach, the entanglement of a pure state is $\sin^2\theta$, where $\theta$ is the angle between the entangled state and the closest separable state of products of normalised qubit states. We consider here a…
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We give a simple way to detect the geometric phase shift and the conditional geometric phase shift with Josephson junction system. Comparing with the previous work(Falcl G, Fazio R, Palma G.M., Siewert J and Verdal V, {\it Nature} {\bf…
We revisit the problem of determining conditions under which a pure state, that evolves under an arbitrary unitary transformation, reaches an orthogonal state in a finite amount of the transformation parameter. Simple geometric…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
In a previous paper we have investigated quantum states evolving into mutually orthogonal states at equidistant times, and the quantum anticipation effect exhibited by measurements at one half step. Here we extend our analyzes of quantum…
In the paper, we show that when a quantum state can be decomposed as a convex combination of locally orthogonal mixed states, its entanglement can be decomposed into the entanglement of these mixed states without losing them. The obtained…
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…
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to…
In this paper we present a necessary and sufficient condition of distinguishability of bipartite quantum states. It is shown that the operators to reliably distinguish states need only rounds of projective measurements and classical…
We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent…
Based on a generic quantum open system model, we study the geometric nature of decoherence by defining a complex-valued geometric phase through stochastic pure states describing non-unitary, non-cyclic and non-adiabatic evolutions. The…
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability…