Entropic uncertainty relations—a survey
By Stephanie Wehner, Andreas J. Winter. 2009
436 citations recorded by the source corpus.
Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, little is known about entropic uncertainty relations with more than two measurement settings. In the present survey, we review known results and open questions.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/73de16899b3c45aff6729a2fe9aa02955edc9eba
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- A framework for non-asymptotic quantum information theory (2012, neutral): “ce by a uniformly distributed bit 2fX;Ygthat is independent of the state ˆ AO . Hence, we consider a joint state ˆ AO = ˆ AO ˇ and a measurement on the Asystem that depends on the classical 1See also [WW10], which oers a comprehensive review of uncertainty relations. 104 7.1 Introduction and Related”
- Advances in quantum cryptography (2019, neutral): “For the sake of self-consistency, we briefly recall the entropic uncertainty relations (EURs) [505, 680], already discussed in Section IX but here adapted to the notation of the present problem.”
- Quantum steering (2019, background): “…bounds on sums of squared mean values are known for many cases of anticommuting observables or mutually unbiased bases (Tóth and Gühne, 2005; Wehner and Winter, 2010; Wu et al., 2009), so one can directly generalize the criteria from above to broader classes of observables on Bob’s side…”
- The infogram: Entropic evidence of the signature of repetitive transients (2016, background): “Interestingly, the sum of the entropies in the time and frequency domains achieves a lower bound, as first shown by Hirschman in 1957 [35], a result known as the “entropic uncertainty principle” [36].”