arXiv subjects
Publications and source records attributed to Karl Svozil.
We propose three criteria for the generation of random digital strings from quantum beam splitters: (i) three or more mutually exclusive outcomes corresponding to the invocation of three- and higher dimensional Hilbert spaces; (ii) the mandatory use of pure states in conjugated bases for preparation and detection; and (iii) the use of entangled singlet (unique) states for elimination of bias.
Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.
As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable.
As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.
We shortly review the construction of knowledge by intrinsic observers. Intrinsic observers are embedded in a system and are inseparable parts thereof. The intrinsic viewpoint has to be contrasted with an extrinsic, "God's eye" viewpoint, from which the system can be observed externally without in any way changing it. This epistemological distinction has concrete, formalizable consequences. One consequence is the emergence of "complementarity" for intrinsic observers, even if the underlying system is totally deterministic (computable). Another consequence is the appearence of time and inertial frames for intrinsic observers. The necessary operational techniques are developed in the context of Cellular Automata. We finish with a somewhat speculative question. Given space-time frames generated by clocks which use sound waves for synchronization; why could supersonic travel not cause time paradoxes?
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
Group theoretic methods to construct all N-particle singlet states by iterative recursion are presented. These techniques are applied to the quantum correlations of four spin one-half particles in their singlet states. Multipartite quantized systems can be partitioned, and their observables grouped and redefined into condensed correlations.
Unlike classical information, quantum knowledge is restricted to the outcome of measurements of maximal observables corresponding to single contexts.
We discuss the question of how to operationally validate whether or not a "hypercomputer" performs better than the known discrete computational models.
Contexts are maximal collections of co-measurable observables "bundled together" to form a "quasi-classical mini-universe." Different notions of contexts are discussed for classical, quantum and generalized urn-automaton systems.
We discuss Doppler shift and interferometric measurements in analogy to the recently reported macroscopic flyby anomalies.
Aesthetics, among other criteria, can be statistically examined in terms of the complexity required for creating and decrypting a work of art. We propose three laws of aesthetic complexity. According to the first law of aesthetic complexity, too condensed encoding makes a decryption of a work of art impossible and is perceived as chaotic by the untrained mind, whereas too regular structures are perceived as monotonous, too orderly and not very stimulating. Thus a necessary condition for an artistic form or design to appear appealing is its complexity to lie within a bracket between monotony and chaos. According to the second law of aesthetic complexity, due to human predisposition, this bracket is invariably based on natural forms; with rather limited plasticity. The third law of aesthetic complexity states that aesthetic complexity trends are dominated by the available resources, and thus also by cost and scarcity.
The trivalent functions of a trit can be grouped into equipartitions of three elements. We discuss the separation of the corresponding functional classes by quantum state identifications.
Correlations in an Einstein-Podolsky-Rosen-Bohm experiment can be made stronger than quantum correlations by allowing a single bit of classical communication between the two sides of the experiment.
The series solution of the behavior of a finite number of physical bodies and Chaitin's Omega number share quasi-algorithmic expressions; yet both lack a computable radius of convergence.
We discuss concrete examples for frame functions and their associated density operators, as well as for non-Gleason type probability measures.
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed in terms of quantum state identification problems based on a proper partitioning of mutually orthogonal sets of states. The question arises whether or not it is possible to encode equibalanced decision problems into quantum systems, so that a single invocation of a filter used for state discrimination suffices to obtain the result.
All experimental tests of Bell-type inequalities and Greenberger-Horne-Zeilinger setups rely on the separate and successive measurement of the terms involved. We discuss possibilities of experimental setups to measure all relevant terms simultaneously in a single experiment and find this to be impossible. One reason is the lack of multi-partite states which are unique in the sense that a measurement of some observable on one particle fixes the value of the corresponding observables of the other particles as well.