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10.1038/ncomms11027 http://scihub22266oqcxt.onion/10.1038/ncomms11027 C4814576!4814576!27006089     free     free     free Deprecated: Implicit conversion from float 231.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 231.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 231.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534       Nat+Commun 2016 ; 7 (ä): ä Nephropedia Template TP {{tp|p=27006089|t=2016. Implementation of quantum and classical discrete fractional Fourier transforms |pdf=|usr=}}{{27006089}} gab.com Text Implementation of quantum and classical discrete fractional Fourier transforms JO: Nat Commun http://www.kidney.de/pget.php?&tw=1&pmid=27006089 #FOAvip Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. Twit Text FOAVip Implementation of quantum and classical discrete fractional Fourier transforms ????Nat Commun http://www.kidney.de/pget.php?&tw=1&pmid=27006089 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=27006089 #FOAvip English Wikipedia <ref>{{Cite pmid|27006089}}</ref> Implementation of quantum and classical discrete fractional Fourier transforms #MMPMID27006089 Weimann S; Perez-Leija A; Lebugle M; Keil R; Tichy M; Gräfe M; Heilmann R; Nolte S; Moya-Cessa H; Weihs G; Christodoulides DN; Szameit A Nat Commun 2016[]; 7 (ä): ä PMID27006089show ga Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. äImplementation of quantum and classical discrete fractional Fourier tr(epmc).pdf DeepDyve Pubget Overpricing