Relative entropy derivation of the uncertainty principle with quantum side information

Details Relative entropy derivation of the uncertainty principle with quantum side information Relative entropy derivation of the uncertainty principle with quantum side information

2011-05-24

arxiv.org/abs/1105.4865v2

Physics

Quantum Physics

8 pages, 1 figure. The main results of this article (with the exception of the MUS examples) are subsumed by our NEWER ARTICLE

Scientific paper

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.

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