Relative entropy derivation of the uncertainty principle with quantum side information
arXiv:1105.4865
Abstract
We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle can be viewed as a data-processing inequality, a special case of the notion that information cannot increase due to evolution in time. This leads to a systematic method for finding the minimum uncertainty states of various entropic uncertainty relations; interestingly such states are intimately connected with the reversibility of time evolution.
8 pages, 1 figure. The main results of this article (with the exception of the MUS examples) are subsumed by our NEWER ARTICLE, arXiv:1112.0543 [quant-ph]. The newer article goes far beyond the present one, giving much more general results and much more conceptual insight
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