A note on Wigner-Yanase skew information-based uncertainty of quantum channels

The variance of quantum channels involving a mixed state gives a hybrid of classical and quantum uncertainties. We seek certain decomposition of variance into classical and quantum parts in terms of the Wigner-Yanase skew information. Generalizing the uncertainty relations for quantum observables to quantum channels, we introduce a new quantity with better quantum mechanical nature to describe the uncertainty relations for quantum channels. We derive several uncertainty relations for quantum channels via variances and the Wigner-Yanase skew information.Comment: 11 pages, 1 figur

Parameterized Multi-observable Sum Uncertainty Relations

The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We establish a series of parameterized uncertainty relations in terms of the parameterized norm inequalities, which improve the exiting variance-based uncertainty relations. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is the common eigenvector of all the observables. Detailed examples are provided to illustrate the tightness of our uncertainty relations.Comment: 12 pages, 3 figure

Anodic electrochemistry of mono- and dinuclear aminophenylferrocene and diphenylaminoferrocene complexes

Two related three-membered series of nonlinear aminophenylferrocene and diphenylaminoferrocene complexes were prepared and characterized by 1H and 13C NMR spectroscopy. The first series consists of 4-(diphenylamino)phenylferrocene (TPA-Fc, 1a), its dimethoxy-substituted tetraphenylphenylenediamine derivative (M2TPPD-Fc, 1c), and the triphenylamine-bridged bis(ferrocenyl) complex (Fc-TPA-Fc, 1b). The second series involves bis(4-methoxyphenyl)aminoferrocene (M2DPA-Fc, 1d), 4-methoxyphenylaminoferrocene (MPA-Fc) with N-phenyl-appended terminal TPA (1e), and the corresponding bis(MPA-Fc) complex with bridging TPA (1f). The structure of complex 1d was further confirmed by single crystal X-ray diffraction. Combined investigations, based on anodic voltammetry, UV-vis-NIR spectroelectrochemistry and density functional theory (DFT) calculations, were conducted to illustrate the influence of the integration of multiple redox-active components on the sequential oxidation of these complexes. The first anodic steps in 1a–1f are localized preferentially on the ferrocenyl units, followed by oxidation of the TPA or TPPD moieties (absent in 1d). Irreversible oxidation of the ferrocene-appended strong donor DPA/MPA units in 1d–1f terminates the anodic series. The one-electron oxidation of the triphenylamine-bridged diferrocenyl (1b) and bis(phenylaminoferrocenyl) (1f) complexes triggers their facile redox disproportionation to dicationic bis(ferrocenium) product

Theoretical calculations of proton emission half-lives based on a deformed Gamow-like model

In the present study, proton emission half-lives have been investigated for the deformed proton emitters with $53\leq Z \leq 83$ in the deformed Gamow-like model, where the deformation effect has been included in the Coulomb potential. The experimental half-lives of proton emitters can be reproduced within a factor of 3.45. For comparison, other results from the universal decay law and the new Geiger-Nuttall law are presented as well. Furthermore, the relevance of the half-lives to the angular momentum $l$ for $^{117}$La, $^{121}$Pr, $^{135}$Tb and $^{141}$Ho has been analyzed, and corresponding possible values of $l$ has been put forward: $l=$3, 3, 4, 4

Effects of grafting on the morphology, physiology, and aerenchyma of balsam pear aboveground under waterlogging stress

The effects of grafting on the morphology, physiology, and aerenchyma of balsam pear aboveground under waterlogging stress were studied using a two-factor randomized block design. At 8 and 16 days, the degree of reduction of grafted balsam pear was lower than those of self-rooted balsam pear, although the height and leaf number of self-rooted and grafted balsam pears were remarkably reduced under waterlogging stress. Compared with self-rooted balsam pear, grafting considerably decreased the malondialdehyde content of balsam pear leaves but substantially increased the activities of antioxidant enzymes (superoxide dismutase, peroxidase, and catalase) and the contents of osmosis-regulating substances (soluble sugar, soluble protein, and proline) in the leaves of balsam pear under waterlogging stress at 4, 8, and 16 days. The stem of grafted balsam pear formed aerenchyma (pith cavity) at 0 days, whereas the stem of self-rooted balsam pear formed aerenchyma at 4 days. The aerenchyma of the stem formed by grafted balsam pear was more developed than that formed by the self-rooted balsam pear under waterlogging stress. The petiole of self-rooted and grafted balsam pears formed aerenchyma at 16 days, and the aerenchyma of grafted balsam pear was more developed than that of self-rooted balsam pear. These results indicated that grafting improved the antioxidant and osmotic regulation ability of balsam pear and enhanced the tolerance of balsam pear to waterlogging stress by enlarging the pith cavity of the stem and petiole of balsam pear