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arXiv:2205.09286 · Physica Scripta

Tighter sum uncertainty relations via metric-adjusted skew information

Hui Li, Ting Gao, Fengli Yan

Published Dec 8, 2022• 12 citations
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Abstract

Abstract In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special cases as Wigner-Yanase-Dyson skew information. In quantifying the uncertainty of channels, we discuss two types of lower bounds and compare the tightness between them, meanwhile, a tight lower bound is given. The uncertainty relations obtained by us are stronger than the existing ones. To illustrate our results, we give several specific examples.

DOI
10.1088/1402-4896/acaa13

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Tighter sum uncertainty relations via (α,β,γ)(α,β,γ)(α,β,γ) weighted Wigner-Yanase-Dyson skew information
We establish tighter uncertainty relations for arbitrary finite observables via (α,β,γ)(α,β,γ)(α,β,γ) weighted Wigner-Yanase-Dyson ((α,β,γ)(α,β,γ)(α,β,γ)WWYD) skew information. The results are also applicable to the (α,γ)(α,γ)(α,γ) weighted Wigner-Yanase-Dyson ((α,γ)(α,γ)(α,γ)WWYD) skew information and the weighted Wigner-Yanase-Dyson (WWYD) skew information. We also present tighter lower bounds of quantum channels and unitary channels via (α,β,γ)(α,β,γ)(α,β,γ) modified weighted Wigner-Yanase-Dyson ((α,β,γ)(α,β,γ)(α,β,γ)MWWYD) skew information. Detailed examples are provided to illustrate tightness of our uncertainty relations.
Abstract We establish tighter uncertainty relations for arbitrary finite observables via ( α , β , γ ) weighted Wigner–Yanase–Dyson (( α , β , γ ) WWYD) skew information. The results are also applicable to the ( α , γ ) weighted Wigner–Yanase–Dyson (( α , γ ) WWYD) skew information and the weighted Wigner–Yanase–Dyson (WWYD) skew information. We also present tighter lower bounds for quantum channels and unitary channels via ( α , β , γ ) modified weighted Wigner–Yanase–Dyson (( α , β , γ ) MWWYD) skew information. Detailed examples are provided to illustrate the tightness of our uncertainty relations.
Abstract Uncertainty principle plays a vital role in quantum physics. The Wigner–Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum channels to arbitrary N quantum channels based on Wigner–Yanase skew information. We illustrate that these uncertainty inequalities are tighter than the existing ones by detailed examples. Especially, we also discuss the uncertainty relations for N unitary channels, which could be regarded as variance-based sum uncertainty relations with respect to any pure state.
Abstract In this paper, we build some uncertainty relations for arbitrary N quantum channels based on the Wigner–Yanase skew information. It is shown that our lower bounds are stronger than the ones proposed by Zhang et al (2021 Phys. Lett. A 387 127029; 2021 Laser Phys. Lett. 18 095204) respectively in all intervals. In particular, we derive several uncertainty relations for N unitary channels. Moreover, we establish several descending sequences of lower bounds for the uncertainty relations of N quantum channels. Detailed examples are provided.