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Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
Quantum Physics · Submitted 26 Jul 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | One of the most important and useful entropic uncertainty relations concerns a $d$ dimensional system and two mutually unbiased measurements. | background 1.00 | 0.05 | 0.04 | asserted 1.00 |
| s1 | In such a setting, the sum of two information entropies is lower bounded by $\ln d$. | background 0.99 | 0.08 | 0.08 | asserted 1.00 |
| s2 | 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. | background 1.00 | 0.05 | 0.04 | asserted 1.00 |
| s3 | 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. | contribution 0.69 | 0.95 | 0.91 | asserted 1.00 |
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Original 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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To this end we partially follow [ref] and [ref] .
Uncertainty related to position and momentum localization of a quantum state · Entropic URs for PCG · 0.90
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