Distance and Similarity Measures in Generalised Quantum Theory

Axiomathes 21 (2):303-313 (2011)
Abstract
A summary of recent experimental results shows that entanglement can be generated more easily than before, and that there are improved chances for its persistence. An eminent finding of Generalised Quantum Theory is the insight that the notion of entanglement can be extended, such that, e.g., psychological or psychophysical problem areas can be included, too. First, a general condition for entanglement to occur is given by the term ‘common prearranged context’. A formalised treatment requires a quantitative definition of the similarity or dissimilarity between two complex structures which takes their internal structures into account. After some specific remarks on distance, metrics, and semi-metrics in mathematics, a procedure is described for setting up a similarity function with the required properties. This procedure is in analogy with the two-step character of measurement and with the well-known properties of perspective notions. A general methodology can be derived for handling perspective notions. Finally, these concepts supply heuristic clues towards a formalised treatment of the notions of ‘meaning’ and ‘interpretation’
Keywords Distance function  Entanglement  Generalised Quantum Theory  Macro-entanglement  Metric  Perspective notions  Semi-metric  Similarity measure
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DOI 10.1007/s10516-010-9137-5
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