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arXiv:2106.01017 · Physics Letters A

Multiple quantum NMR in solids as a method of determination of Wigner–Yanase skew information

Serge I. Doronin, Edward B. Fel’dman, I. D. Lazarev

Published May 26, 2021• 6 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2021.127458

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The change of the total Wigner-Yanase skew information of two coupled two-level atoms interacting with two-mode squeezed vacuum state field was investigated. The results showed that when the squeezed factor was smaller,the interaction between atoms and field,the dipole-dipole interaction of two atoms determined evolution period of the total Wigner-Yanase skew information together; enhancing the dipoledipole interaction of two atoms could resist the loss of the total Wigner-Yanase skew information; the squeezed factor of light field played an important role in the loss of the total Wigner-Yanase skew information,and when the squeezed factor was bigger,the total Wigner-Yanase skew information of atoms would lose completely.
The Wigner-Yanase skew information was proposed to quantify the information contained in quantum states with respect to a conserved additive quantity, and it was later extended to the Wigner-Yanase-Dyson skew informations. Recently, the Wigner-Yanase-Dyson skew informations have been recognized as valid resource measures for the resource theory of asymmetry, and their properties have been investigated from a resource-theoretic perspective. The Wigner-Yanse-Dyson skew informations have been further generalized to a class called metric-adjusted skew informations, and this general family of skew informations have also been found to be valid asymmetry monotones. Here, we analyze this general family of the skew informations from an operational point of view by utilizing the fact that they are valid asymmetry resource monotones. We show that such an approach allows for clear physical meanings as well as simple proofs of some of the basic properties of the skew informations. Notably, we constructively prove that any type of skew information cannot be superadditive, where the violation of the superadditivity had been only known for a specific class of skew informations with numerical counterexamples. We further show a weaker version of superadditivity relation applicable to the general class of the skew informations, which proves a conjecture made for the Wigner-Yanase skew information as a special case. We finally discuss an application of our results for a situation where quantum clocks are distributed to multiple parties.
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.