48 results for Svozil, K, Report

• ### How Random Is Quantum Randomness? An Experimental Approach

#### Calude, CS; Dinneen, MJ; Dumitrescu, M; Svozil, K (2009-12-22)

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The University of Auckland Library

Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness". We base our experimental approach on algorithmic information theory which provides characterizations of algorithmic random sequences in terms of the degrees of incompressibility of their finite prefixes. Algorithmic random sequences are incomputable, but the converse implication is false. We have performed tests of randomness on pseudo-random strings (finite sequences) of length $2^{32}$ generated with software (Mathematica, Maple), which are cyclic (so, strongly computable), the bits of $\pi$, which is computable, but not cyclic, and strings produced by quantum measurements (with the commercial device Quantis and by the Vienna IQOQI group). Our empirical tests indicate quantitative differences, some statistically significant, between computable and incomputable sources of "randomness".

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• ### Randomness Relative to Cantor Expansions

#### Calude, C.S; Staiger, L; Svozil, K (2003-04)

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The University of Auckland Library

Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. Such sequences occur in various physical contexts, in which the coding of experimental outcome varies with scale. When can such a sequence be called random? In this paper we offer a solution to the above question using the approach to randomness proposed by Algorithmic Information Theory.

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• ### Quantum Queries Associated with Equi-Partitioning of States and Multipartite Relational Encoding Across Space-Time

#### Svozil, K (2015)

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The University of Auckland Library

In the first part of this paper we analyze possible quantum computational capacities due to quantum queries associated with equi-partitions of pure orthogonal states. Special emphasis is given to the parity of product states and to functional parity. The second part is dedicated to a critical review of the relational encoding of multipartite states across (space-like separated) space-time regions; a property often referred to as “quantum nonlocality.”

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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 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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• ### 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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• ### On Coloring the Rational Quantum Sphere

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

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The University of Auckland Library

We discuss types of colorings of the rational quantum sphere similar to the one suggested recently by Meyer [1], in particular the consequences for the Kochen-Specker theorem and for the correlation functions of entangled subsystems.

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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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• ### 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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• ### Computational Universes

#### Svozil, K (2003-05)

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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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• ### 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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• ### 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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• ### n-ary Quantum Information Defined by State Partitions

#### Svozil, K (2002-05)

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The University of Auckland Library

We define a measure of quantum information which is based on state partitions. Properties of this measure for entangled many-particle states are discussed. k particles specify k “nits” in such a way that k mutually commuting measurements of n-ary observables are necessary to determine the information.

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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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• ### Aesthetic Complexity

#### Svozil, K (2008-04)

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The University of Auckland Library

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.

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• ### Kochen-Specker 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 Library

We present a stronger variant of the Kochen-Specker 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 three-dimensional Hilbert space.

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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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