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arXiv · 2107.12431

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

Łukasz Rudnicki·Stephen P. Walborn
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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\'enyi entropies applied to these discretized observables and prove that such a scheme does also admit the uncertainty relation mentioned above.

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Łukasz Rudnicki, Stephen P. Walborn. 2021-07-26. Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts. https://doi.org/10.1103/physreva.104.042210

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