Discrete Entropic Uncertainty Relations Associated with FRFT

Guanlei Xu, Xiaotong Wang, Lijia Zhou, Limin Shao, Xiaogang Xu

Navgation department of Dalian Naval Academy, Dalian, China, 116018..
Ocean department of Dalian Naval Academy, Dalian, China, 116018.

DOI: 10.4236/jsip.2013.43B021                

Abstract

Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.

Keywords

Discrete Fractional Fourier Transform (DFRFT); Uncertainty Principle; Rényi Entropy; Shannon Entropy

Conflicts of Interest

The authors declare no conflicts of interest.

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