In [Phys. Rev. Lett. 114, 250401 (2015)] the sharing of non-locality by multiple observers was demonstrated through the quantum violation of Clauser-Horne-Shimony-Halt inequality. In this paper we provide a scheme for sharing of non-locality and non-trivial preparation contextuality sequentially through the quantum violation of a family of Bell's inequalities where Alice and Bob perform 2 n−1 and n numbers of measurements of dichotomic observables respectively. For this, we consider that Alice always performs projective measurement and multiple Bobs sequentially perform unsharp measurement. We show that when Bob's choices of measurement settings are unbiased, maximum two Bobs can sequentially share the non-locality through the violation of our inequalities. Further, we show that the local bound of the aforementioned family of inequalities gets reduced if non-trivial preparation non-contextuality assumptions are further imposed. Then there is a chance to share the non-trivial preparation contextuality for more number of Bobs than that of non-locality. We demonstrate that the non-trivial preparation contextuality can be sequentially shared by arbitrary numbers of Bob for unbiased choices of his measurement settings.

In a recent Letter [PRL, 113, 050401 (2014)], it is shown that the quantum violation of a threetime Leggett-Garg inequality (LGI) for a dichotomic qutrit system can exceed the Lüders bound. This is obtained by using a degeneracy breaking projective measurement rule which the authors termed as von Neumann rule. Such violation can even approach the algebraic maximum in the asymptotic limit of system size. In this paper, we question the implication of such violation of Lüders bound and its conceptual relevance in LG scenario. We note an important fact that the basis for implementing the proposed von Neumann rule for a degenerate observable is non-unique and show that the violation of Lüders bound is crucially dependent on the choice of basis. Further, we demonstrate the violation of Lüders bound of the simplest non-contextual inequality (NCI) which is in contrast to the reasoning provided in the aforementioned Letter. This result further raises the doubts regarding the validity of the proposed rule as a viable projective measurement. We discuss the relevance of such results with respect to the usual quantum violation of LGI and NCI.

For tumor to grow beyond 1-2 mm size, tumor recruits new blood vessels referred as angiogenesis; therefore, targeting angiogenesis can be a promising strategy to suppress cancer progression. In this study, in order to develop a good angiogenesis model, we investigated effect of Dalton's lymphoma on angiogenesis and further monitored the role of melatonin on regulation of angiogenesis. To evaluate angiogenesis, endothelial cells were isolated from main thoracic aorta and cultured in vitro in the presence or absence of Dalton's lymphoma supplemented with or without melatonin to monitor their role on its proliferation and migration, a hallmark of angiogenesis. Chick chorioallantoic membrane as well as mice mesentery which allows in vivo studies of tumor angiogenesis and testing of anti-angiogenic molecules was used to validate the in vitro analysis. To further extend our understanding about the regulation of the angiogenesis, we evaluated expression of tissue inhibitor of metalloproteinases 3, vascular endothelial growth factor, vascular endothelial growth factor receptor, and fibroblast growth factor in Dalton's lymphoma cells and mesentery by semiquantitative and quantitative reverse transcription polymerase chain reaction analysis. Dalton's lymphoma ascites induced significant increase in endothelial cell proliferation, migration, and sprouting of the tertiary branching in chorioallantoic membrane and mesentery of Dalton's lymphoma-bearing mice, whereas melatonin treatment led to their inhibition in a dose-dependent manner. Semiquantitative and quantitative reverse transcription polymerase chain reaction analysis of melatonin-treated Dalton's lymphoma cells and mesentery tissue clearly demonstrated restoration of angiogenesis-related genes tissue inhibitor of metalloproteinases 3 and reduction of vascular endothelial growth factor, vascular endothelial growth factor receptor, and fibroblast growth factor messenger RNA expression. Taken together, our results strongly demonstrate that Dalton's lymphoma provides pro-angiogenic environment leading to significant increase in angiogenesis, and further melatonin treatment reduced the Dalton's lymphoma ascites-induced angiogenesis implying that Dalton's lymphoma can serve as a very good model to study angiogenesis as well as for screening of drugs that can target angiogenesis.

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