Please use this identifier to cite or link to this item: https://doi.org/10.1063/1.2943685
Title: Higher entropic uncertainty relations for anti-commuting observables
Authors: Wehner, S.
Winter, A. 
Issue Date: 2008
Citation: Wehner, S., Winter, A. (2008). Higher entropic uncertainty relations for anti-commuting observables. Journal of Mathematical Physics 49 (6) : -. ScholarBank@NUS Repository. https://doi.org/10.1063/1.2943685
Abstract: Uncertainty relations provide one of the most powerful formulations of the quantum mechanical principle of complementarity. Yet, very little is known about such uncertainty relations for more than two measurements. Here, we show that sufficient unbiasedness for a set of binary observables, in the sense of mutual anticommutation, is good enough to obtain maximally strong uncertainty relations in terms of the Shannon entropy. We also prove nearly optimal relations for the collision entropy. This is the first systematic and explicit approach to finding an arbitrary number of measurements for which we obtain maximally strong uncertainty relations. Our results have immediate applications to quantum cryptography. © 2008 American Institute of Physics.
Source Title: Journal of Mathematical Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/112449
ISSN: 00222488
DOI: 10.1063/1.2943685
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