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arXiv:2006.09600 · Communications in Theoretical Physics

Uncertainty relations based on Wigner–Yanase skew information

Xiaofen Huang, Tinggui Zhang, Naihuan Jing

Published Jun 9, 2020• 7 citations
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Abstract

Abstract In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner–Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds. We then propose new weighted uncertainty relations for two noncompatible observables. Two separable criteria via skew information are also obtained.

DOI
10.1088/1572-9494/ab892f

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