83 research outputs found
A Non-Probabilistic Model of Relativised Predictability in Physics
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 [1] 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.Comment: 10 page
A Quantum Random Number Generator Certified by Value Indefiniteness
In this paper we propose a quantum random number generator (QRNG) which
utilizes an entangled photon pair in a Bell singlet state, and is certified
explicitly by value indefiniteness. While "true randomness" is a mathematical
impossibility, the certification by value indefiniteness ensures the quantum
random bits are incomputable in the strongest sense. This is the first QRNG
setup in which a physical principle (Kochen-Specker value indefiniteness)
guarantees that no single quantum bit produced can be classically computed
(reproduced and validated), the mathematical form of bitwise physical
unpredictability. The effects of various experimental imperfections are
discussed in detail, particularly those related to detector efficiencies,
context alignment and temporal correlations between bits. The analysis is to a
large extent relevant for the construction of any QRNG based on beam-splitters.
By measuring the two entangled photons in maximally misaligned contexts and
utilizing the fact that two rather than one bitstring are obtained, more
efficient and robust unbiasing techniques can be applied. A robust and
efficient procedure based on XORing the bitstrings together---essentially using
one as a one-time-pad for the other---is proposed to extract random bits in the
presence of experimental imperfections, as well as a more efficient
modification of the von Neumann procedure for the same task. Some open problems
are also discussed.Comment: 25 pages, 3 figure
What Makes a Computation Unconventional?
A coherent mathematical overview of computation and its generalisations is
described. This conceptual framework is sufficient to comfortably host a wide
range of contemporary thinking on embodied computation and its models.Comment: Based on an invited lecture for the 'Symposium on
Natural/Unconventional Computing and Its Philosophical Significance' at the
AISB/IACAP World Congress 2012, University of Birmingham, July 2-6, 201
Classical, quantum and biological randomness as relative unpredictability
International audienceWe propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness — its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity. Abstract We propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness—its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity
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