Coherence and complementarity based on modified generalized skew information

Wu, Zhaoqi; Zhang, Lin; Fei, Shao-Ming; Li‐Jost, Xianqing

doi:10.1007/s11128-020-02651-3

Cited by 16 publications

(18 citation statements)

References 66 publications

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“…Comparing (12) in Theorem 4.1 with (19) in Theorem 4 of [68], we see that the mean value E U [CGP S (U )] of skew information-based CGP for random unitary channels coincides with average skew information-based coherence E ρ [C I (ρ)] for random quantum mixed states. This fact can be explained as follows.…”

Section: Cgp As a Random Variable Over The Unitary Group Under Skew I...mentioning

confidence: 90%

“…The past few years have witnessed a great interest in quantifying quantum coherence by utilizing various distance measures such as relative entropy, l 1 -norm, intrinsic randomness, robustness of coher-ence, max-relative entropy, fidelity, affinity, skew information, generalized α-z-relative Rényi entropy, logarithmic coherence number, Schatten-p-norm and Fisher information, etc. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. On the other hand, the problem of coherence distillation and coherence dilution have also been discussed [22][23][24][25][26][27][28], and a complete theory of one-shot coherence distillation has been formulated [29].…”

Section: Introductionmentioning

confidence: 99%

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Skew information-based coherence generating power of quantum channels

Wu,

Zhang,

Fei

et al. 2022

Preprint

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We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. We define the measure of coherence generating power (CGP) for a generic quantum channel to be the average coherence generated by the quantum channel acting on a uniform ensemble of incoherent states based on the skew information-based coherence measure. We present explicitly the analytical formulae of the CGP for any arbitrary finite dimensional unitary channels. We derive the mean value of the CGP over the unitary groups and investigate the typicality of the normalized CGP. Furthermore, we give an upper bound of the CGP for the convex combinations of unitary channels. Detailed examples are provided to calculate exactly the values of the CGP for the unitary channels related to specific quantum gates and for some qubit channels.

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Section: Cgp As a Random Variable Over The Unitary Group Under Skew I...mentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Skew information-based coherence generating power of quantum channels

Wu,

Zhang,

Fei

et al. 2022

Preprint

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“…The MGWYD skew information Q α,β (ρ, K) is also convex in ρ when α, β ∈ [0, 1] with α + 2β ≤ 1 and 2α + β ≤ 1 [25]. By using the Lieb's theorem [16,55], it can be easily obtained that C α,β (ρ, K) is concave in ρ for α, β ≥ 0, α+β ≤ 1.…”

Section: The Total Uncertainty Of Quantum Channels Based On Mgvmentioning

confidence: 99%

“…Therefore, it is desirable to introduce the corresponding definitions of the above-mentioned skew information for pseudo-Hermitian and/or PT-symmetric quantum mechanics [18][19][20][21][22][23]. By considering an arbitrary operator which may be non-Hermitian, Dou and Du [8] have introduced the modified Wigner-Yanase-Dyson (MWYD) skew information, while Wu, Zhang and Fei [24,25] have further introduced the modified generalized Wigner-Yanase-Dyson (MGWYD) skew information.…”

Section: Introductionmentioning

confidence: 99%

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

Xu,

Wu,

Fei

2022

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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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“…By considering state-channel interaction, in [41] Luo and Sun defined a quantity I ρ (Φ) and its dual one J ρ (Φ), and explored the complementarity relation between them. Wu, Zhang and Fei introduced the non-Hermitian extension of the GWYD skew information and generalized the complementarity relation to a more general case in [42,43].…”

Section: Introductionmentioning

confidence: 99%

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

Xu,

Wu,

Fei

2022

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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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Coherence and complementarity based on modified generalized skew information

Cited by 16 publications

References 66 publications

Skew information-based coherence generating power of quantum channels

Skew information-based coherence generating power of quantum channels

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

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

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