A generalization of Schrödinger’s uncertainty relation described by the Wigner–Yanase skew information

Li, Qian; Cao, Huaixin; Du, Hongliang

doi:10.1007/s11128-014-0896-6

Cited by 10 publications

(3 citation statements)

References 13 publications

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“…After that, Furuichi [26] derived a Schrödinger-type uncertainty relation using the quantity U ρ (H), and a generalization of Schrödinger's uncertainty relation based on Wigner-Yanase skew information is presented in Ref. [27].…”

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confidence: 99%

Sum uncertainty relations based on Wigner–Yanase skew information

Chen¹,

Fei²,

Long³

2016

Quantum Inf Process

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We study sum uncertainty relations for arbitrary finite N quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented. 1 chenbin5134@163.com 2

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confidence: 99%

Sum uncertainty relations based on Wigner–Yanase skew information

Chen¹,

Fei²,

Long³

2016

Quantum Inf Process

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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: 97%

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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“…[8] and references therein), etc. It is worth noting that there are many other ways to formulate uncertainty relations, such as in terms of entropies [9,10,11,12,13,14], by use of majorization approach [15,16,17,18,19,20], based on the skew information [21,22,23] and the notion of fine-grained uncertainty relation [24,25,26]. Throughout the paper, we only focus on the variance-based sum uncertainty relations.…”

Section: Introductionmentioning

confidence: 99%