47 results for Svozil, K, Report

  • Physical versus Computational Complementarity I

    Calude, C; Calude, E; Svozil, K; Yu, S (1996-06)

    Report
    The University of Auckland Library

    The dichotomy between endophysical/intrinsic and exophysical/extrinsic perception concerns the question of how a model|mathematical, logical, computational|universe is perceived from inside or from outside, [71, 65, 66, 59, 60, 68, 67]. This distinction goes back in time at least to Archimedes, reported to have asked for a point outside the world from which one could move the earth. An exophysical perception is realized when the system is laid out and the experimenter peeps at the relevant features without changing the system. The information flows on a one-way road: from the system to the experimenter. An endophysical perception can be realized when the experimenter is part of the system under observation. In such a case one has a two-way informational flow; measurements and entities measured are interchangeable and any attempt to distinguish between them ends up as a convention. The general conception dominating the sciences is that the physical universe is perceivable only from inside. This view reduces the exophysical perception to a theoretical illusion. The more plausible perception, i.e. an endophysical one, suffers from a “self-referential" disease as any intrinsic measurement causes uncontrolled, and maybe uncontrollable, “disturbances" to the entity intended to be measured. This paper, the first in a proposed series, discusses some limitations and trade-offs between endophysical/intrinsic and exophysical/extrinsic perceptions, in both physical and computational contexts. We are building our work on Moore “gedanken" experiments [50] in which the universe is modeled by a finite deterministic automaton. A new type of computational complementarity, which mimics the state of quantum entanglement, is introduced and contrasted with Moore's computational complementarity. Computer simulations of both types of computational complementarity are developed for four-states Moore automata.

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  • Interferometric Information Gain Versus Interaction-Free Measurement

    Krenn, G; Summhammer, J; Svozil, K (2000-02)

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    The University of Auckland Library

    Interaction-free measurement schemes with ideal Mach-Zehnder interferometers promised to distinguish absorptive samples with lower average absorption than simple transmission schemes. We show that this is only true for an ensemble of two kinds of samples, where one kind is highly absorptive and the other is highly transmissive. As soon as a third kind of sample with intermediate transmission is introduced, but no phase shift is permitted, the cost of information gain in terms of absorbed particles in the samples is higher in the interferometric scheme. We also investigate the general case of samples with a continuous range of transmission and phase shift values, such that an interferometer's ability to measure both sample characteristics can be exploited. With an interferometer the number of principally distinguishable samples increases linearly with the number of probe particles, but with a simple transmission setup it in- creases as the square root. When wishing to distinguish twice as many samples from a continuous sample distribution with an interferometric scheme, the number of absorbed particles per sample only doubles, but it quadruples with a simple transmission scheme.

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  • A Non-Probabilistic Model of Relativised Predictability in Physics

    Abbott, AA; Calude, CS; Svozil, K (2015)

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    The University of Auckland Library

    Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed inherent unpredictability of measurement outcomes. In this paper we continue the programme started in developing a general, non-probabilistic model of (un)predictability in physics. We present a more refined model that is capable of studying different degrees of “relativised” unpredictability. This model is based on the ability for an agent, acting via uniform, effective means, to predict correctly and reproducibly the outcome of an experiment using finite information extracted from the environment. We use this model to study further the degree of unpredictability certified by different quantum phenomena, showing that quantum complementarity guarantees a form of relativised unpredictability that is weaker than that guaranteed by Kochen-Specker-type value indefiniteness. We exemplify further the difference between certification by complementarity and value indefiniteness by showing that, unlike value indefiniteness, complementarity is compatible with the production of computable sequences of bits.

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  • A Variant of the Kochen-Specker Theorem Localising Value Indefiniteness (Revision1)

    Abbott, AA; Calude, CS; Svozil, K (2015)

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    The University of Auckland Library

    The Kochen-Specker theorem proves the inability to assign, simultaneously, noncontextual definite values to all (of a finite set of) quantum mechanical observables in a consistent manner. If one assumes that any definite values behave noncontextually, one can nonetheless only conclude that some observables (in this set) are value indefinite. In this paper we prove a variant of the Kochen-Specker theorem showing that, under the same assumption of noncontextuality, if a single one-dimensional projection observable is assigned the definite value 1, then no one-dimensional projection observable that is incompatible (i.e., non-commuting) with this one can be assigned consistently a definite value. Unlike standard proofs of the Kochen-Specker theorem, in order to localise and show the extent of value indefiniteness this result requires a constructive method of reduction between Kochen-Specker sets. If a system is prepared in a pure state |yi, then it is reasonable to assume that any value assignment (i.e., hidden variable model) for this system assigns the value 1 to the observable projecting onto the onedimensional linear subspace spanned by |yi, and the value 0 to those projecting onto linear subspaces orthogonal to it. Our result can be interpreted, under this assumption, as showing that the outcome of a measurement of any other incompatible one-dimensional projection observable cannot be determined in advance, thus formalising a notion of quantum randomness.

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  • The min-max Principle Generalizes Tsirelson's Bound

    Filipp, S; Svozil, K (2004-04)

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    The University of Auckland Library

    Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type inequalities.

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  • Single Particle Interferometric Analogues of Multipartite Entanglement

    Svozil, K (2004-01)

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    The University of Auckland Library

    Based on research by Reck et al. [1] and Zukowski et al. [2], preparation and measurement configurations for the singlet states of two and three two- and three-state particles are enumerated in terms of multiport interferometers.

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  • Proposed Direct Test of Quantum Contextuality

    Svozil, K (2009-02)

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    The University of Auckland Library

    Quantum contextually can be directly tested by an Einstein-Podolsky-Rosen-type experiment of two spin one and higher particles in a singlet state. The two associated contexts are “interlinked” by a common observable.

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  • Quantum Randomness and Value Indefiniteness

    Calude, C.S; Svozil, K (2006-11)

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    The University of Auckland Library

    As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable.

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  • Solution of Problem No. 10769

    Svozil, K (2000-02)

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    The University of Auckland Library

    We review previous solutions of problem nr. 10769 posed by Christian Blatter

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  • Embedding Quantum Universes into Classical Ones

    Calude, C.S; Hertling, P.H; Svozil, K (1997-05)

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    The University of Auckland Library

    Do the partial order and lattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Re-phrased, how far might a classical understanding of quantum mechanics be, in principle, possible? A celebrated result by Kochen and Specker answers the above question in the negative. However, this answer is just one among different possible ones, not all negative. It is our aim to discuss the above question in terms of mappings of quantum worlds into classical ones, more specifically, in terms of embeddings of quantum logics into classical logics; depending upon the type of restrictions imposed on embeddings the question may get negative or positive answers.

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  • Communication Cost of Breaking the Bell Barrier

    Svozil, K (2004-12)

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    The University of Auckland Library

    Adaptive as well as nonadaptive, memoryless protocols are presented which give rise to stronger than quantum correlations at the cost of the exchange of a single classical bit.

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  • Quantum Scholasticism: On Quantum Contexts, Counterfactuals, and the Absurdities of Quantum Omniscience

    Svozil, K (2009-02)

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    The University of Auckland Library

    Unlike classical information, quantum knowledge is restricted to the outcome of measurements of maximal observables corresponding to single contexts.

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  • On the Unpredictability of Individual Quantum Measurement Outcomes

    Abbott, AA; Calude, CS; Svozil, K (2014)

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    The University of Auckland Library

    We develop a general, non-probabilistic model of prediction which is suitable for assessing the (un)predictability of individual physical events. We use this model to provide, for the first time, a rigorous proof of the unpredictability of a class of individual quantum measurement outcomes, a well-known quantum attribute postulated or claimed for a long time. We prove that quantum indeterminism—formally modelled as value indefiniteness—-is incompatible with the supposition of predictability: value indefinite observables are unpredictable. The proof makes essential use of a strengthened form of the Kochen-Specker theorem proven previously to identify value indefinite observables. As a result, quantum unpredictability, like the Kochen-Specker theorem, relies on three assumptions: compatibility with quantum mechanical predictions, non-contextuality, and the value definiteness of observables corresponding to the preparation basis of a quantum state. Finally, quantum unpredictability is used to prove that quantum randomness is "maximally incomputable" and to discuss a real model of hypercomputation whose computational power has yet to be determined. The paper ends with a further open problem.

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  • Quantum music

    Putz, V; Svozil, K (2015)

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    The University of Auckland Library

    We consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby, we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.

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  • Logical Equivalence Between Generalized Urn Models and Finite Automata

    Svozil, K (2002-02)

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    The University of Auckland Library

    To every generalized urn model there exists a finite (Mealy) automaton with identical propositional calculus. The converse is true as well.

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  • Quantum Theory Looks at Time Travel

    Greenberger, D.M; Svozil, K (2005-06)

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    The University of Auckland Library

    We introduce a quantum mechanical model of time travel which includes two figurative beam splitters in order to induce feedback to earlier times. This leads to a unique solution to the paradox where one could kill one’s grandfather in that once the future has unfolded, it cannot change the past, and so the past becomes deterministic. On the other hand, looking forwards towards the future is completely probabilistic. This resolves the classical paradox in a philosophically satisfying manner.

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  • Science at the Crossroad Between Randomness and Determinism

    Svozil, K (2000-05)

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    The University of Auckland Library

    Time and again, man’s understanding of Nature is at the crossroad between total worldcomprehension and total randomness. It is suggested that not only are the preferences influenced by the theories and models of today, but also by the very personal subjective inclinations of the people involved. The second part deals with the principle of self-consistency and its consequences for totally deterministic systems.

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  • Some Observations Concerning the Plasticity of Nonlocal Quantum Correlations Exceeding Classical Expectations

    Svozil, K (2009-02)

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    The University of Auckland Library

    The quantum correlations of two or more entangled particles present the possibility of stronger-than-classical outcome coincidences. We review the standard cases of two and four two-state particles. We also investigate two-partite correlations of spin one and spin three-half quanta in a state satisfying a uniqueness property in the sense that knowledge of an outcome of one particle observable entails the certainty that, if this observable were measured on the other particle(s) as well, the outcome of the measurement would be a unique function of the outcome of the measurement performed.

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  • Computational Universes

    Svozil, K (2003-05)

    Report
    The University of Auckland Library

    Suspicions that the world might be some sort of a machine or algorithm existing “in the mind” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.

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  • Counterfactual Effect, the Halting Problem, and the Busy Beaver Function

    Calude, C.S; Dinneen, Michael; Svozil, K (1999-07)

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    The University of Auckland Library

    Using the counterfactual effect, we demonstrate that with better than 50% chance we can determine whether an arbitrary universal Turing machine will halt on an arbitrarily given program. As an application we indicate a probabilistic method for computing the busy beaver function| a classical uncomputable function. These results suggest a possibility of going beyond the Turing barrier.

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