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Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts

Authors :
Rudnicki, ��ukasz
Walborn, Stephen P.
Publication Year :
2021
Publisher :
arXiv, 2021.

Abstract

One of the most important and useful entropic uncertainty relations concerns a $d$ dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $\ln d$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain, with the help of periodic coarse graining. Here we consider the whole family of R��nyi entropies applied to these discretized observables and prove that such a scheme does also admit the uncertainty relation mentioned above.<br />7 pages, submitted to PRA

Details

Database :
OpenAIRE
Accession number :
edsair.doi...........e90b8e57d41eafd39ea752d461acf544
Full Text :
https://doi.org/10.48550/arxiv.2107.12431