Details
| Original language | English |
|---|---|
| Article number | 033043 |
| Number of pages | 6 |
| Journal | Physical Review Research |
| Volume | 6 |
| Issue number | 3 |
| Publication status | Published - 9 Jul 2024 |
Abstract
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this paper, we provide a family of versatile generalizations of this relation. Our proof methods build on a deep connection between entropic uncertainties and interpolation inequalities for the doubly stochastic map that links probability distributions in two measurement bases. In contrast to the original relation, our generalization also incorporates the von Neumann entropy of the underlying quantum state. These results can be directly used to bound the extractable randomness of a source-independent quantum random number generator in the presence of fully quantum attacks, to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.
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In: Physical Review Research, Vol. 6, No. 3, 033043, 09.07.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Entropic uncertainty principle for mixed states
AU - Rotundo, Antonio F.
AU - Schwonnek, René
N1 - Publisher Copyright: © 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
PY - 2024/7/9
Y1 - 2024/7/9
N2 - The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this paper, we provide a family of versatile generalizations of this relation. Our proof methods build on a deep connection between entropic uncertainties and interpolation inequalities for the doubly stochastic map that links probability distributions in two measurement bases. In contrast to the original relation, our generalization also incorporates the von Neumann entropy of the underlying quantum state. These results can be directly used to bound the extractable randomness of a source-independent quantum random number generator in the presence of fully quantum attacks, to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.
AB - The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this paper, we provide a family of versatile generalizations of this relation. Our proof methods build on a deep connection between entropic uncertainties and interpolation inequalities for the doubly stochastic map that links probability distributions in two measurement bases. In contrast to the original relation, our generalization also incorporates the von Neumann entropy of the underlying quantum state. These results can be directly used to bound the extractable randomness of a source-independent quantum random number generator in the presence of fully quantum attacks, to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.
UR - http://www.scopus.com/inward/record.url?scp=85198226220&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2303.11382
DO - 10.48550/arXiv.2303.11382
M3 - Article
AN - SCOPUS:85198226220
VL - 6
JO - Physical Review Research
JF - Physical Review Research
SN - 2643-1564
IS - 3
M1 - 033043
ER -