Relative entropy derivation of the uncertainty principle with quantum side information

2011/05/24 by Patrick J. Coles, Coles, Patrick J., Li Yu +4
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #quant-ph

paper · pdf · doi:10.48550/arxiv.1105.4865

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

openalex publication_date 2011/05/24 · arxiv created 2011/12/07 · arxiv updated 2011/12/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Related

• Quantum relative entropy uncertainty relation
• Entropic uncertainty assisted by temporal memory
• Lower and upper bounds for unilateral coherence and applying them to the entropic uncertainty relations
• Tightening the entropic uncertainty relations for multiple measurements and applying it to quantum coherence
• Protecting the entropic uncertainty lower bound in Markovian and non-Markovian environment via additional qubits