相关论文: Decomposition Theorem for State Property Systems

We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…

We analyze a class of entangled states for bipartite $d \otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is…

The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…

Coherent states with large amplitudes are traditionally thought of as the best quantum mechanical approximation of classical behavior. Here we argue that, far from being classical, coherent state are in fact highly entangled. We demonstrate…

Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to…

The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…

We prove a converse theorem for split even special orthogonal groups over finite fields. This is the only case left on converse theorems of split classical groups and the difficulty is the existence of the outer automorphism. In this paper,…

We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal,…

We illustrate some problems that are related to the existence of an underlying linear structure at the level of the property lattice associated with a physical system, for the particular case of two explicitly separated spin 1/2 objects…

Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…

We present a two-part program for state space decomposition. States are classified into entanglement classes based on local unitary transformations, and then characterized as elements of topological spaces using the language of fibre…

Klauder's recent generalization of the harmonic oscillator coherent states [J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems, requiring some additional structure if applied to systems with degeneracies. The author…

We prove a converse theorem for the case of quasi-split non-split even special orthogonal groups over finite fields. There are two main difficulties which arise from the outer automorphism and non-split part of the torus. The outer…

The Holant theorem is a powerful tool for studying the computational complexity of counting problems in the Holant framework. Due to the great expressiveness of the Holant framework, a converse to the Holant theorem would itself be a very…

A necessary and sufficient condition for characterization and quantification of entanglement of any bipartite Gaussian state belonging to a special symmetry class is given in terms of classicality measures of one-party states. For Gaussian…

We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…

We analyze condition of orthogonality between optical Schrodinger cat-like-states constructed as superposition of two coherent states. We show that the orthogonality condition leads to quantization of values of a naturally emerging…

We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.

Ergodic systems, being indecomposable are important part of the study of dynamical systems but if a system is not ergodic, it is natural to ask the following question: Is it possible to split it into ergodic systems in such a way that the…

In this short note, we will explain that the good moduli space morphisms behave as if they are proper when we consider sheaf operations, though they are not separated. For example, the decomposition theorem and the base change theorem hold…