相关论文: Representation Systems and Quantum Structures
A general principle of `causal duality' for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
In this review paper I present two geometric constructions of distinguished nature, one is over the field of complex numbers $\mathbb{C}$ and the other one is over the two elements field $\mathbb{F}_2$. Both constructions have been employed…
Classical and quantum perturbations can be described in terms of marginal distribution functions in the framework of tomographic cosmology. In particular, the so called Radon transformation and the mode-parametric quantum oscillator…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
A possible causal solution to the problem of providing a spacetime description of the transmission of signals in quantum entangled states is described using a `bimetric' spacetime structure, in which the quantum entanglement measurements…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. An…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
We study the general representations of positive partial transpose (PPT) states in ${\cal C}^K \otimes {\cal C}^M \otimes {\cal C}^N$. For the PPT states with rank-$N$ a canonical form is obtained, from which a sufficient separability…
Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
According to the stochastic-quantum correspondence, a quantum system can be understood as a stochastic process unfolding in an old-fashioned configuration space based on ordinary notions of probability and `indivisible' stochastic laws,…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…