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

• URL: http://arxiv.org/abs/2107.12431v1
• Date: Mon, 26 Jul 2021 18:48:26 GMT
• Title: Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Authors: {\L}ukasz Rudnicki and Stephen P. Walborn
• Abstract summary: In a $d$ dimensional system and two mutually unbiased measurements, 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. 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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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