47 results for Svozil, K, Report

A NonProbabilistic Model of Relativised Predictability in Physics
Abbott, AA; Calude, CS; Svozil, K (2015)
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The University of Auckland LibraryLittle 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, nonprobabilistic 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 KochenSpeckertype 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 KochenSpecker Theorem Localising Value Indefiniteness (Revision1)
Abbott, AA; Calude, CS; Svozil, K (2015)
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The University of Auckland LibraryThe KochenSpecker 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 KochenSpecker theorem showing that, under the same assumption of noncontextuality, if a single onedimensional projection observable is assigned the definite value 1, then no onedimensional projection observable that is incompatible (i.e., noncommuting) with this one can be assigned consistently a definite value. Unlike standard proofs of the KochenSpecker theorem, in order to localise and show the extent of value indefiniteness this result requires a constructive method of reduction between KochenSpecker 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 onedimensional projection observable cannot be determined in advance, thus formalising a notion of quantum randomness.
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Single Particle Interferometric Analogues of Multipartite Entanglement
Svozil, K (200401)
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The University of Auckland LibraryBased 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 threestate particles are enumerated in terms of multiport interferometers.
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Proposed Direct Test of Quantum Contextuality
Svozil, K (200902)
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The University of Auckland LibraryQuantum contextually can be directly tested by an EinsteinPodolskyRosentype 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 (200611)
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The University of Auckland LibraryAs computability implies value definiteness, certain sequences of quantum outcomes cannot be computable.
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Solution of Problem No. 10769
Svozil, K (200002)
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The University of Auckland LibraryWe 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 (199705)
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The University of Auckland LibraryDo the partial order and lattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Rephrased, 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 (200412)
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The University of Auckland LibraryAdaptive 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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On the Unpredictability of Individual Quantum Measurement Outcomes
Abbott, AA; Calude, CS; Svozil, K (2014)
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The University of Auckland LibraryWe develop a general, nonprobabilistic 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 wellknown 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 KochenSpecker theorem proven previously to identify value indefinite observables. As a result, quantum unpredictability, like the KochenSpecker theorem, relies on three assumptions: compatibility with quantum mechanical predictions, noncontextuality, 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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On the Brightness of the Thomson lamp. A Prolegomenon to Quantum Recursion Theory
Svozil, K (200904)
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The University of Auckland LibrarySome quantum cryptographic protocols can be implemented with specially prepared chocolate balls, others protected by value indefiniteness cannot. Similarities and differences of cryptography with quanta and chocolate are discussed. Motivated by these considerations it is proposed to certify quantum random number generators and quantum cryptographic protocols by value indefiniteness. This feature, which derives itself from Belland KochenSpecker type arguments, is only present in systems with three or more mutually exclusive outcomes.
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Logical Equivalence Between Generalized Urn Models and Finite Automata
Svozil, K (200202)
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The University of Auckland LibraryTo 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 Scholasticism: On Quantum Contexts, Counterfactuals, and the Absurdities of Quantum Omniscience
Svozil, K (200902)
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The University of Auckland LibraryUnlike classical information, quantum knowledge is restricted to the outcome of measurements of maximal observables corresponding to single contexts.
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Quantum music
Putz, V; Svozil, K (2015)
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The University of Auckland LibraryWe consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby, we give particular emphasis to its nonclassical aspects, such as coherent superposition and entanglement.
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Quantum Theory Looks at Time Travel
Greenberger, D.M; Svozil, K (200506)
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The University of Auckland LibraryWe 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 (200005)
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The University of Auckland LibraryTime 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 selfconsistency and its consequences for totally deterministic systems.
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Computational Universes
Svozil, K (200305)
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The University of Auckland LibrarySuspicions 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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Some Observations Concerning the Plasticity of Nonlocal Quantum Correlations Exceeding Classical Expectations
Svozil, K (200902)
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The University of Auckland LibraryThe quantum correlations of two or more entangled particles present the possibility of strongerthanclassical outcome coincidences. We review the standard cases of two and four twostate particles. We also investigate twopartite correlations of spin one and spin threehalf 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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Counterfactual Effect, the Halting Problem, and the Busy Beaver Function
Calude, C.S; Dinneen, Michael; Svozil, K (199907)
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The University of Auckland LibraryUsing 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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KochenSpecker Theorem Revisited and Strong Incomputability of Quantum Randomness
Abbott, A.A; Calude, C.S.; Conder, J.; Svozil, K (2012)
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The University of Auckland LibraryWe present a stronger variant of the KochenSpecker theorem in which some quantum observables are identiﬁed to be provably value indeﬁnite. This result is utilised for the construction and certiﬁcation of a dichotomic quantum random number generator operating in a threedimensional Hilbert space.
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nary Quantum Information Defined by State Partitions
Svozil, K (200205)
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The University of Auckland LibraryWe define a measure of quantum information which is based on state partitions. Properties of this measure for entangled manyparticle states are discussed. k particles specify k “nits” in such a way that k mutually commuting measurements of nary observables are necessary to determine the information.
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