An Operational Characterization for Optimal Observation of Potential Properties in Quantum Theory and Signal Analysis |
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Authors: | Sven Aerts |
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Institution: | (1) Center Leo Apostel for Interdisciplinary Studies (CLEA) and Foundations of the Exact Sciences (FUND), Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium |
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Abstract: | Quantum logic introduced a paradigm shift in the axiomatization of quantum theory by looking directly at the structural relations
between the closed subspaces of the Hilbert space of a system. The one dimensional closed subspaces correspond to testable
properties of the system, forging an operational link between theory and experiment. Thus a property is called actual, if
the corresponding test yields “yes” with certainty. We argue a truly operational definition should include a quantitative
criterion that tells us when we ought to be satisfied that the test yields “yes” with certainty. This question becomes particularly pressing when we inquire how the usual definition can be extended to cover potential,
rather than actual properties. We present a statistically operational candidate for such an extension and show that its representation
automatically captures some essential Hilbert space structure. If it is the nature of observation that is responsible for
the Hilbert space structure, then we should be able to give examples of theories with scope outside the domain of quantum
theory, that employ its basic structure, and that describe the optimal extraction of information. We argue signal analysis
is such an example.
This work was supported by the Flemish Fund for Scientific Research (FWO) project G.0362.03N. |
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Keywords: | Potential property Quantum logic Quantum theory Signal analysis Optimal observation |
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