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Cited by 166Quantum Mechanics and ApplicationsQuantum Information and CryptographyNoncommutative and Quantum Gravity Theories

Universal Uncertainty Relations

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Friedland, Shmuel, Gheorghiu, Vlad, Gour, Gilad·2013·Physical Review Letters
DOI 10.1103/physrevlett.111.230401
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Abstract

Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs entropic measures to quantify the lack of knowledge associated with measuring noncommuting observables. However, there is no fundamental reason for using entropies as quantifiers; any functional relation that characterizes the uncertainty of the measurement outcomes defines an uncertainty relation. Starting from a very reasonable assumption of invariance under mere relabeling of the measurement outcomes, we show that Schur-concave functions are the most general uncertainty quantifiers. We then discover a fine-grained uncertainty relation that is given in terms of the majorization order between two probability vectors, significantly extending a majorization-based uncertainty relation first introduced in M. H. Partovi, Phys. Rev. A 84, 052117 (2011). Such a vector-type uncertainty relation generates an infinite family of distinct scalar uncertainty relations via the application of arbitrary uncertainty quantifiers. Our relation is therefore universal and captures the essence of uncertainty in quantum theory.

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  • The robustness measure in entanglement theory measures the amount of noise that can be added to an entangled state before it becomes unentangled (separable).

    “The measure of robustness [23, 33, 34] in entanglement theory measures the amount of noise that can be added to an entangled state before it becomes unentangled (separable).”

    From Reversible Framework for Quantum Resource Theories (2015) · cites this paper as [33]

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Authors
Friedland, S., Gheorghiu, V., & Gour, G.
Affiliations
  • University of Illinois Chicago (US)
  • University of Waterloo (CA)
  • University of Calgary (CA)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2013-12-03
Volume
111
Issue
23
Pages
230401-230401
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.111.230401
OpenAlex
W2046535252
Cited by
166
References
29
Citations by year
2026: 4 · 2025: 11 · 2024: 13 · 2023: 7 · 2022: 13 · 2021: 8 · 2020: 11 · 2019: 19 · 2018: 17 · 2017: 12 · 2016: 23 · 2015: 13 · 2014: 14 · 2013: 1
FWCI
8.75
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
Keywords
uncertainty relations, Schur-concave functions, majorization, non-commuting observables, quantum measurement

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