Uncertainty relations based on Wigner–Yanase skew information

Huang, Xiaofen; Zhang, Tinggui; Jing, Naihuan

doi:10.1088/1572-9494/ab892f

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2023

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“…It is worth noting that they can constitute various uncertainty relations [40][41][42][43][44][45][46][47][48][49]. They shed new light on our understanding of uncertainty.…”

Section: Introductionmentioning

confidence: 95%

Uncertainty relation of successive measurements based on Wigner–Yanase skew information

Zhang¹,

Wei²,

duan³

et al. 2021

Commun. Theor. Phys.

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Wigner–Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity. We present the uncertainty principle for two successive projective measurements in terms of Wigner–Yanase skew information based on a single quantum system. It could capture the incompatibility of the observables, i.e. the lower bound can be nontrivial for the observables that are incompatible with the state of the quantum system. Furthermore, the lower bound is also constrained by the quantum Fisher information. In addition, we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state, respectively.

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“…It is worth noting that they can constitute various uncertainty relations [40][41][42][43][44][45][46][47][48][49]. They shed new light on our understanding of uncertainty.…”

Section: Introductionmentioning

confidence: 95%