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Communications in Theoretical Physics

Tighter sum uncertainty relations via ( α , β , γ ) weighted Wigner–Yanase–Dyson skew information

Cong Huai Xu, Zhaoqi Wu, Shao-Ming Fei

Published Jan 23, 2024• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1572-9494/ad216b

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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.
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Uncertainty principle is one of the most essential features of quantum mechanics, and it reveals the intrinsic difference that distinguishes the quantum world from the classical world. In this paper, we focus on the uncertainty relations based on metric-adjusted skew information. By making full use of the norm property, we establish an uncertainty relation for arbitrary finite nnn observables based on metric-adjusted skew information, and we give two new uncertainty relations for arbitrary finite NNN quantum channels based on metric-adjusted skew information. For arbitrary two observables and two channels, the uncertainty relations we give are not only better than the uncertainty relations detailed in [Quantum Inf. Process. 20, 72 (2021)], but also are the equations. The equation of the uncertainty relation is more accurate than the inequation of the usual uncertainty relation, which has important advantages in the application of quantum information technology, such as quantum communication and the quantum precision measurement. Meanwhile, our results are suitable to Wigner-Yanase-Dyson skew information that is a special metric-adjusted skew information and Wigner-Yanase skew information that is a special Wigner-Yanase-Dyson skew information. Some examples about Wigner-Yanase-Dyson skew information are given and show that the new lower bounds are tighter. The results play an important role in quantum information processing in this paper.
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