Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Statistical Physics

An Informational Characterization of Schrödinger's Uncertainty Relations

Shunlong Luo, Zhengmin Zhang

Published Feb 3, 2004• 40 citations
Publisher
DOI
10.1023/b:joss.0000013971.75667.c8

Related papers

Explorations into the Schrodinger Uncertainty Relation

Nathan Steiger, Jean-François S. Van Huele

Bulletin of the American Physical Society•Oct 17, 2008•0 citations

On Covariance and Quantum Fisher Information

Shunlong Luo

For a quantum state and a set of observables, we can construct an associated covariance matrix and a natural quantum Fisher information matrix. These two matrices characterize the uncertainty and information content of the observables in the relevant state. An inequality between these two matrices is established. This inequality may be interpreted as a general quantification of the Heisenberg uncertainty principle from a statistical estimation perspective. In particular, it implies a new uncertainty relation which refines the celebrated Schrödinger uncertainty relation.

Theory of Probability and Its Applications•Jan 1, 2009•2 citations

Role of information theoretic uncertainty relations in quantum theory

Petr Jizba B, Jacob Dunningham, Jaewoo Joo

Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.

•Apr 1, 2015•35 citations

An improvement of Schrödinger's uncertainty relation

Pintu Bhunia, Mohammad Sal Moslehian

Physics Letters A•May 19, 2025•3 citations

Schrödinger uncertainty relation and convexity for the monotone pair skew information

Chul Ki Ko, Hyun Jae Yoo

Furuichi and Yanagi showed a Schrödinger uncertainty relation for the Wigner-Yanase-Dyson skew information, which is a special monotone pair skew information. In this paper, we give a Schrödinger uncertainty relation based on a monotone pair skew information, and extend the result of Furuichi and Yanagi. Moreover, we show that some monotone pair skew information becomes a metric adjusted skew information and therefore the convexity of it follows from known results.

Tohoku Mathematical Journal•Jan 1, 2014•2 citations

Stronger Schrödinger-like uncertainty relations

Qiu-Cheng Song, Cong‐Feng Qiao

arXiv:1504.01137•Physics Letters A•Jul 12, 2016•49 citations
For a quantum state and a set of observables, we can construct an associated covariance matrix and a natural quantum Fisher information matrix. These two matrices characterize the uncertainty and information content of the observables in the relevant state. An inequality between these two matrices is established. This inequality may be interpreted as a general quantification of the Heisenberg uncertainty principle from a statistical estimation perspective. In particular, it implies a new uncertainty relation which refines the celebrated Schrödinger uncertainty relation.
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.