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- W3105743888 abstract "While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is a certain splitting of the total Hilbert space and its recursive iterations to further iterated subdivisions. This paper explores some implications for associated probability measures (in the classical sense of measure theory), specifically their fractal components. We identify a fractal scale $s$ in a family of Borel probability measures $mu$ on the unit interval which arises independently in quantum information theory and in wavelet analysis. The scales $s$ we find satisfy $sin mathbb{R}_{+}$ and $snot =1$, some $s <1$ and some $s>1$. We identify these scales $s$ by considering the asymptotic properties of $mu(J) /| J| ^{s}$ where $J$ are dyadic subintervals, and $| J| to0$." @default.
- W3105743888 created "2020-11-23" @default.
- W3105743888 creator A5058575589 @default.
- W3105743888 date "2007-10-01" @default.
- W3105743888 modified "2023-10-13" @default.
- W3105743888 title "The measure of a measurement" @default.
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- W3105743888 doi "https://doi.org/10.1063/1.2794561" @default.
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