Applications of FFT and Structured Matrices

Emiris, Ioannis Z.; Pan, Victor Y.

doi:10.1201/9781584888239-c18

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2015

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“…An n×m Toeplitz matrix is completely determined by the n + m − 1 elements on its first row and column. This structure implies that only O(n log n) time for encoding is required for this subclass of RLCs [38]. Additionally, these codes also asymptotically approach the GV bound (see Supplementary Material for a proof).…”

Section: Error-correcting Codementioning

confidence: 84%

Experimental Quantum Fingerprinting

Xu,

Arrazola,

Wei

et al. 2015

Preprint

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Quantum communication holds the promise of creating disruptive technologies that will play an essential role in future communication networks. For example, the study of quantum communication complexity has shown that quantum communication allows exponential reductions in the information that must be transmitted to solve distributed computational tasks. Recently, protocols that realize this advantage using optical implementations have been proposed. Here we report a proof of concept experimental demonstration of a quantum fingerprinting system that is capable of transmitting less information than the best known classical protocol. Our implementation is based on a modified version of a commercial quantum key distribution system using off-the-shelf optical components over telecom wavelengths, and is practical for messages as large as 100 Mbits, even in the presence of experimental imperfections. Our results provide a first step in the development of experimental quantum communication complexity.

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Section: Error-correcting Codementioning

confidence: 84%