The uncertainty of quantum channels in terms of variance

Sun, Yuan; Li, Nan

doi:10.1007/s11128-020-02972-3

Cited by 25 publications

(38 citation statements)

References 51 publications

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“…There are also many ways to describe uncertainty relations, such as entropy [3][4][5][6][7], variance [8][9][10][11] and majorization techniques [12][13][14][15]. In particular, the quantum uncertainty can also be characterized by skew information.…”

Section: Introductionmentioning

confidence: 99%

Tighter uncertainty relations based on $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

Xu¹,

Wu²,

Fei³

2022

Preprint

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We use a novel formation to illustrate the (α, β, γ) modified weighted Wigner-Yanase-Dyson ((α, β, γ) MWWYD) skew information of quantum channels. By using operator norm inequalities, we explore the sum uncertainty relations for arbitrary N quantum channels and for unitary channels. These uncertainty inequalities are shown to be tighter than the existing ones by a detailed example. Our results are also applicable to the modified weighted Wigner-Yanase-Dyson (MWWYD) skew information and the (α, γ) modified weighted Wigner-Yanase-Dyson ((α, γ) MWWYD) skew information of quantum channels as special cases.

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Section: Introductionmentioning

confidence: 99%

Tighter uncertainty relations based on $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

Xu¹,

Wu²,

Fei³

2022

Preprint

View full text Add to dashboard Cite

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“…where [A, B] = AB − BA and ∆Ω = ψ|Ω 2 |ψ − ψ|Ω|ψ 2 is the standard deviation of an observable Ω. Many different characterizations and quantifications of quantum uncertainty have been proposed in terms of entropy [3][4][5][6][7][8][9][10][11], variance [12][13][14][15], under successive measurements [16][17][18][19], and with majorization techniques [9,[20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Sum uncertainty relations based on $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew information

Xu,

Wu,

Fei

2022

Preprint

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We introduce (α, β, γ) weighted Wigner-Yanase-Dyson ((α, β, γ) WWYD) skew information and (α, β, γ) modified weighted Wigner-Yanase-Dyson ((α, β, γ) MWWYD) skew information. We explore the sum uncertainty relations for arbitrary N mutually noncommutative observables based on (α, β, γ) WWYD skew information. A series of uncertainty inequalities are derived. We show by detailed example that our results cover and improve the previous ones based on the original Wigner-Yanase (WY) skew information. Finally, we establish new sum uncertainty relations in terms of the (α, β, γ) MWWYD skew information for arbitrary N quantum channels.

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“…In addition, Dou and Du [7,8] have proposed a Heisenberg-type uncertainty relation and a Schrödinger-type uncertainty relation based on the modified variance. Sun and Li [9] have proposed the total uncertainty of quantum channels in terms of the modified variance.…”

Section: Introductionmentioning

confidence: 99%

“…We give an extension of the trade-off relation between the total uncertainty of quantum channels and the entanglement fidelity. By recalling two important information quantities, the entropy exchange [51] and coherent information [52], we also generalize the relations between the total uncertainty of quantum channels and the entropy exchange/coherent information introduced in [9] to a more general case.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information

Xu,

Wu,

Fei

2022

Preprint

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Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. By using modified generalized variance (MGV), and modified generalized Wigner-Yanase-Dyson skew information (MGWYD), we identify the total and quantum uncertainty of quantum channels. The elegant properties of the total uncertainty of quantum channels are explored in detail. In addition, we present a trade-off relation between the total uncertainty of quantum channels and the entanglement fidelity, and establish the relationships between the total uncertainty and entropy exchange/coherent information. Detailed examples are given to the explicit formulas of the total uncertainty and the quantum uncertainty of quantum channels. Moreover, utilizing a realizable experimental measurement scheme by using the Mach-Zehnder interferometer proposed in [65], we discuss how to measure the total/quantum uncertainty of quantum channels for pure states.

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The uncertainty of quantum channels in terms of variance

Cited by 25 publications

References 51 publications

Tighter uncertainty relations based on $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

Tighter uncertainty relations based on $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

Sum uncertainty relations based on $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew information

Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information

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