The Generalized Uncertainty Principle

• URL: http://arxiv.org/abs/2003.08705v2
• Date: Tue, 19 Jan 2021 01:50:33 GMT
• Title: The Generalized Uncertainty Principle
• Authors: Jun-Li Li, Cong-Feng Qiao
• Abstract summary: The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation.
• Score: 0.6091702876917281
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed.

Related papers

• Precision bounds for multiple currents in open quantum systems [37.69303106863453]
  We derivation quantum TURs and KURs for multiple observables in open quantum systems undergoing Markovian dynamics. Our bounds are tighter than previously derived quantum TURs and KURs for single observables. We also find an intriguing quantum signature of correlations captured by the off-diagonal element of the Fisher information matrix.
  arXiv  Detail & Related papers  (2024-11-13T23:38:24Z)
• Observing tight triple uncertainty relations in two-qubit systems [21.034105385856765]
  We demonstrate the uncertainty relations in two-qubit systems involving three physical components with the tight constant $2/sqrt3$. Our results provide a new insight into understanding the uncertainty relations with multiple observables and may motivate more innovative applications in quantum information science.
  arXiv  Detail & Related papers  (2024-10-08T11:24:24Z)
• Uncertainty relations based on state-dependent norm of commutator [0.0]
  We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is strongly supported by numerical evidence.
  arXiv  Detail & Related papers  (2024-06-18T05:16:45Z)
• Linear Opinion Pooling for Uncertainty Quantification on Graphs [21.602569813024]
  We propose a novel approach that represents (epistemic) uncertainty in terms of mixtures of Dirichlet distributions. The effectiveness of this approach is demonstrated in a series of experiments on a variety of graph-structured datasets.
  arXiv  Detail & Related papers  (2024-06-06T13:10:37Z)
• Measurement incompatibility is strictly stronger than disturbance [44.99833362998488]
  Heisenberg argued that measurements irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. This article shows that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance. However, we exhibit a toy theory, termed the minimal classical theory (MCT), that is a counterexample for the converse implication.
  arXiv  Detail & Related papers  (2023-05-26T13:47:00Z)
• Parameterized Multi-observable Sum Uncertainty Relations [9.571723611319348]
  We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is a common eigenvector of all the observables.
  arXiv  Detail & Related papers  (2022-11-07T04:36:07Z)
• What is nonclassical about uncertainty relations? [0.0]
  Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. We show that for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve.
  arXiv  Detail & Related papers  (2022-07-24T17:19:47Z)
• Equivalence principle violation from large scale structure [0.0]
  We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle. We observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched.
  arXiv  Detail & Related papers  (2022-05-21T11:17:15Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• A Universal Formulation of Uncertainty Relation for Error and Disturbance [0.9479435599284545]
  We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable.
  arXiv  Detail & Related papers  (2020-04-13T17:57:41Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.