منابع مشابه
Basis-neutral Hilbert-space analyzers
Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes - a critical task for spatial-mode multiplexing and quantum communication - basis-specific principles are invoked that are altoge...
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We discuss novel clustering methods that are based on mapping data points to a Hilbert space by means of a Gaussian kernel. The *rst method, support vector clustering (SVC), searches for the smallest sphere enclosing data images in Hilbert space. The second, quantum clustering (QC), searches for the minima of a potential function de*ned in such a Hilbert space. In SVC, the minimal sphere, when ...
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Nowak [N], improving a theorem due to A. N. Dranishnikov, G. Gong, V. Lafforgue, and G. Yu [DGLY], gave a characterization of coarse embeddability of general metric spaces into a Hilbert space using a result of Schoenberg on negative definite kernels. He used this characterization to show that the spaces Lp(μ) coarsely embed into a Hilbert space for p < 2. In this article, we show that lp does ...
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Wormhole boundary conditions for the Wheeler-DeWitt equation can be derived from the path integral formulation. It is proposed that the wormhole wave function must be square integrable in the maximal analytic extension of minisuperspace. Quantum wormholes can be invested with a Hilbert-space structure, the inner product being naturally induced by the minisuperspace metric, in which the Wheeler-...
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A non-Hermitian complex symmetric 2 × 2-matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseuxexpanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular b...
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ژورنال
عنوان ژورنال: Scientific Reports
سال: 2017
ISSN: 2045-2322
DOI: 10.1038/srep44995