Improved quantum entropic uncertainty relations

Zhi-Hua Chen, Zhi-Hao Ma, Yunlong Xiao, and Shao-Ming Fei

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Submission date: 09. Jan. 2019
Pages: 16
published in: Physical review / A, 98 (2018) 4, art-no. 042305 
DOI number (of the published article): 10.1103/PhysRevA.98.042305
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Abstract:
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and the tighter state-dependent one based on the majorization techniques. The analytical results for qubit and qutrit systems with two or three measurement settings are explicitly derived, with detailed examples showing that they outperform the existing bounds. The case with the presence of quantum memory is also investigated.