Improved Uncertainty Relation in the Presence of Quantum Memory

Yunlong Xiao, Naihuan Jing, Shao-Ming Fei, and Xianqing Li-Jost

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Submission date: 04. Jan. 2017
Pages: 7
published in: Journal of physics / A, 49 (2016) 49, art-no. 49LT01 
DOI number (of the published article): 10.1088/1751-8113/49/49/49LT01
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Abstract:
In Coles-Piani’s recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty relation and find the exact dependence on all first d largest overlaps between two measurements on any d-dimensional Hilbert space. The corresponding entropic uncertainty principle in the presence of quantum memory is also derived. Our bounds are strictly tighter than previous entropic bounds.