Related papers: Geometric Quantization from a Coherent State Viewp…
The aim of this article is to study the functorial properties of the ``formal geometric quantization'' procedure which is defined for non-compact Hamiltonian manifolds (when the moment map is proper). For this purpose, we introduce a…
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
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…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
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…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
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…
We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase…
This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to…
The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the…
An adiabatic cyclic evolution of control parameters of a quantum system ends up with a holonomic operation on the system, determined entirely by the geometry in the parameter space. The operation is given either by a simple phase factor (a…
At a fixed point in spacetime (say, x_0), gravitational phase space consists of the space of symmetric matrices F^{ab} [corresponding to the canonical momentum pi^{ab}(x_0) and of symmetric matrices {G_{ab}}[corresponding to the canonical…
Everett's concept of relative state is used to introduce a geometric phase that depends nontrivially on entanglement in a pure quantum state. We show that this phase can be measured in multiparticle interferometry. A correlation-dependent…
Quantifying quantum coherence is a key task in the resource theory of coherence. Here we establish a good coherence monotone in terms of a state conversion process, which automatically endows the coherence monotone with an operational…
We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this…
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…