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On the Uncertainty Relations

J. R. Croca

Springer eBooksJan 1, 19954 citations

Stronger uncertainty relations with arbitrarily tight upper and lower bounds

Jun Zhang, Yang Zhang, Chang‐shui Yu

We utilize quantum superposition principle to establish the upper and lower bounds on the stronger uncertainty relation [Phys. Rev. Lett. 113, 260401 (2014)], i.e., the ”weighted-like” sum of the variances of observables. Our bounds include some free parameters which not only guarantee the nontrivial bounds but also can effectively control the bounds as tightly as one expects. Especially, these parameters don’t obviously depend on the state and observables. It also implies one advantage of our method that any nontrivial bound can always be tight enough. In addition, we generalize both bounds to the uncertainty relation with multiple observables, but the perfect tightness is not changed. Examples are given to illustrate the tightness of our bounds in each case.We utilize quantum superposition principle to establish the upper and lower bounds on the stronger uncertainty relation [Phys. Rev. Lett. 113, 260401 (2014)], i.e., the ”weighted-like” sum of the variances of observables. Our bounds include some free parameters which not only guarantee the nontrivial bounds but also can effectively control the bounds as tightly as one expects. Especially, these parameters don’t obviously depend on the state and observables. It also implies one advantage of our method that any nontrivial bound can always be tight enough. In addition, we generalize both bounds to the uncertainty relation with multiple observables, but the perfect tightness is not changed. Examples are given to illustrate the tightness of our bounds in each case.

Jul 27, 20161 citation

Uncertainty Relations and Their Applications

Frontiers research topicsJan 1, 20220 citations

A Stronger Multi-observable Uncertainty Relation

Qiu-Cheng Song, Jun-Li Li, Guang-Xiong Peng +1 more

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for N incompatible observables stronger than the simple generalization of an existing uncertainty relation for two observables. Further comparisons of our uncertainty relation with other related ones for spin- and spin-1 particles indicate that the obtained uncertainty relation gives a better lower bound.Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for N incompatible observables stronger than the simple generalization of an existing uncertainty relation for two observables. Further comparisons of our uncertainty relation with other related ones for spin- and spin-1 particles indicate that the obtained uncertainty relation gives a better lower bound.

arXiv:1701.01072Scientific ReportsMar 20, 201747 citations

Strengthening the uncertainty and the reverse uncertainty relation limits

Mahmoud Youssef Abd‐Rabbou, Cong‐Feng Qiao

arXiv:2508.02036Quantum Information ProcessingNov 29, 20251 citation

Strong Variance-Based Uncertainty Relations and Uncertainty Intervals

Yunlong Xiao, Naihuan Jing, Bing Yu +2 more

Uncertainty relations occupy a fundamental position in quantum mechanics. We propose stronger variance-based uncertainty relations for the product and sum of variances of two incompatible observables in a finite dimensional Hilbert space. It is shown that the new uncertainty relations provide near-optimal state-dependent bounds, which can be useful for quantum metrology, entanglement detection etc. in quantum information theory. It is further shown that the uncertainty relations are related to the spreads of the distribution of measurement outcomes caused by incompatible observables. Intuitively, this means that the ability of learning the distribution has both the upper and lower bounds. Combination of these bounds provides naturally an uncertainty interval which captures the essence of uncertainty in quantum theory. Finally, we explain how to employ entropic uncertainty relations to derive lower bounds for the product of variances of incompatible observables.Uncertainty relations occupy a fundamental position in quantum mechanics. We propose stronger variance-based uncertainty relations for the product and sum of variances of two incompatible observables in a finite dimensional Hilbert space. It is shown that the new uncertainty relations provide near-optimal state-dependent bounds, which can be useful for quantum metrology, entanglement detection etc. in quantum information theory. It is further shown that the uncertainty relations are related to the spreads of the distribution of measurement outcomes caused by incompatible observables. Intuitively, this means that the ability of learning the distribution has both the upper and lower bounds. Combination of these bounds provides naturally an uncertainty interval which captures the essence of uncertainty in quantum theory. Finally, we explain how to employ entropic uncertainty relations to derive lower bounds for the product of variances of incompatible observables.

Oct 5, 20160 citations

Stronger uncertainty relations with improvable upper and lower bounds

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