Some Inequalities for Wigner–Yanase Skew Information

Luo, Shunlong; Sun, Yuan

doi:10.1007/978-3-319-97798-0_16

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Obviously I(ρ A) < I(λ(ρ) A) and I(ρ) < I(λ(ρ))1

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2024

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“…According to the definition of SSI and SSSI, there are I(ρ, A π ) ⩾ I(Λ(ρ), A π ) and I(ρ) ⩾ I(Λ(ρ)) . If the system Hilbert space is two-dimensional, Λ † (A π ) = A π and Λ † ((A π ) 2 ) = (A π ) 2 are equivalent [13]. Therefore the conditions can be simplified on two-dimensional system.…”

Section: Obviously I(ρ A) < I(λ(ρ) A) and I(ρ) < I(λ(ρ))mentioning

confidence: 99%

The standard symmetrized skew information and its applications

Ren,

Luo,

2024

J. Phys. A: Math. Theor.

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In this paper, we propose two new measures: one is symmetrized skew information and the other one is standard symmetrized skew information. Firstly, we prove their properties, such as non-negativity, convexity, invariance, additivity, monotonicity and strong monotonicity. Next, we conduct research on relationships between standard symmetrized skew information and several well-known measures in one-qubit state, aiming to compare their similarities and diﬀerences. In addition, standard symmetrized skew information is used to study quantum uncertainty. We also give the deﬁnition of standard symmetrized skew information of assistance, and provide it a straightforward operational explanation for better understanding. Finally, standard symmetrized skew information can be applied to detect entanglement.

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Section: Obviously I(ρ A) < I(λ(ρ) A) and I(ρ) < I(λ(ρ))mentioning

confidence: 99%