Basic Structures of RelativisticWave Functions

Sihong Shao, Zhendong Li, Wenjian Liu

Vladimir I. Hahanov, Eugenia I. Litvinova, Svetlana V. Chumachenko +1 more

Qubit models for defining the structures and functionalities are developed to improve the performance of the analysis of digital devices by increasing the dimension of the data and memory structures. The basic concepts, terminology, definitions, necessary for the implementation of quantum computation in the practice of modeling computer structures, are introduced. The examples proving the efficiency of qubit data structures for parallel operations on the data are represented.

Egidio Landi Degl’Innocenti

Anna Jenčová

We study higher order quantum maps in the context of a *-autonomous category of affine subspaces. We show that types of higher order maps can be identified with certain Boolean functions that we call type functions. By an extension of this identification, the algebraic structure of Boolean functions is inherited by some sets of quantum objects including higher order maps. Using the Mobius transform, we assign to each type function a poset whose elements are labelled by subsets of indices of the involved spaces. We then show that the type function corresponds to a comb type if and only if the poset is a chain. We also devise a procedure for decomposition of the poset to a set of basic chains from which the type function is constructed by taking maxima and minima of concatenations of the basic chains in different orders. On the level of higher order maps, maxima and minima correspond to affine mixtures and intersections, respectively.

Paul E. Hussar

Elio Conte

In quantum mechanics a wave function is connected to a quantum system. This abstract entity represents a description of the quantum state of this system. The wave function is a complex-valued probability amplitude and the probabilities for the possible results of measurements made on the system can be derived from it . In the present paper it is demonstrated that the tentative often adopted from scholars to attribute a wave function as representation of a mental state in current quantum cognition studies cannot be accepted. A mental state is a so complex structure , depending contextually at each instant from a so complex structure of inner and subjective elements and psychological and neurological components, to exclude its representation by a simple and elementary wave function, The mental state may be represented by a quantum wave function that, owing of the complex structure of the mental state, has an intrinsic indetermination and fluctuation of the basic probability amplitudes to respond to the basic notion of intrinsecally , incompletely specified system that was introduced by P. T. Landsberg in 1961. As consequence a simple quantum wave function cannot be adopted and instead an averaging statistical formulation is absolutely required. Therefore, the subsequent quantum statistical theory is formulated.