相关论文: Decomposition Theorem for State Property Systems

Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition,…

A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition…

An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a…

We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known…

We show that the natural mathematical structure to describe a physical entity by means of its states and its properties within the Geneva-Brussels approach is that of a state property system. We prove that the category of state property…

A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive…

The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some…

We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a…

In their 1936 founding paper on quantum logic, Birkhoff and von Neumann postulated that the lattice describing the experimental propositions concerning a quantum system is orthocomplemented. We prove that this postulate fails for the…

Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental…

We prove that every symmetric separable state admits a convex decomposition into symmetric pure product states. While the result is not new in itself, here we focus on convex geometry. We discuss the decomposition in the context of…

A property of a system is called actual, if the observation of the test that pertains to that property, yields an affirmation with certainty. We formalize the act of observation by assuming that the outcome correlates with the state of the…

We propose a toy-model theory, that mimics various characteristic features of quantum mechanics. Unlike the toy-models previously studied in the literature, our toy-model allows for an observer to have a full knowledge of a system's real…

An eigenstate decoherence hypothesis states that each individual eigenstate of a large closed system is locally classical-like. We extend this hypothesis to account for a typically extremely short time scale of decoherence. The extension…

We give a short proof of an improved version of the Effros Open Mapping Principle via a shift-compactness theorem (also with a short proof), involving `sequential analysis' rather than separability, deducing it from the Baire property in a…

We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition…

We examine uniqueness of equilibrium states for the natural extension of a topologically exact, non-uniformly expanding, local homeomorphism with a H\"older continuous potential function. We do this by applying general techniques developed…

In this paper an extended CPR decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive structures is proven. This decomposition theorem is applied to give a geometric description of the…

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context…

The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As…