The Existence of Quantum Entanglement Catalysts

Without additional resources, it is often impossible to transform one entangled quantum state into another with local quantum operations and classical communication. Jonathan and Plenio [Phys. Rev. Lett. 83, 3566(1999)] presented an interesting example showing that the presence of another state, called a catalyst, enables such a transformation without changing the catalyst. They also pointed out that in general it is very hard to find an analytical condition under which a catalyst exists. In this paper we study the existence of catalysts for two incomparable quantum states. For the simplest case of $2\times 2$ catalysts for transformations from one $4\times 4$ state to another, a necessary and sufficient condition for existence is found. For the general case, we give an efficient polynomial time algorithm to decide whether a $k\times k$ catalyst exists for two $n\times n$ incomparable states, where $k$ is treated as a constant.Comment: 12 pages. Presentation part improved. Main results unchanged. Essentially the journal versio

Ki-67 Regulates Cell Cycle Progression and Heterochromatin Organization

A subset of eukaryotic heterochromatin is located around the nucleoli, and this localization is correlated with gene silencing. Although there is some evidence for trans-acting factors organizing genomic loci around the nucleolus, the characterization of proteins and /or RNAs involved in perinculeolar heterochromatin localization and maintenance is incomplete. Notably, the mammalian female inactive X chromosome, a well-studied model of facultative heterochromatin, frequently resides in the perinucleolar regions during mid to late S phase. The disruption of the Xi–nucleolus association results in the erosion of heterochromatin compartment and silencing, which renders it a good model to investigate the mechanism and biological relevance of heterochromatin organization around the nucleolus. This dissertation will present evidence showing that Ki-67 regulates inactive X (Xi) chromosome association with nucleoli, maintains Xi heterochromatic structures, and regulates cell cycle progression, in cell-type-specific manner dependent on checkpoint proficiency. Ki-67 protein plays roles in heterochromatin organization during interphase. Upon Ki-67 depletion, a subset of Xi in human female hTERT-RPE1 moved away from nucleolus and displayed several features of compromised heterochromatin maintenance. These chromatin alterations were limited to Xi chromosomes localized away from the nuclear lamina and were not observed in virally transformed 293T cells upon Ki-67 depletion. Furthermore, I demonstrated that the different Xi heterochromatin alteration responses result from cell-type-specific reduced proportion of cells in S phase upon Ki-67 depletion. In human hTERT-RPE1, WI-38, IMR90, hTERT-BJ cell lines, depletion of Ki-67 slowed entry into S phase and coordinately downregulated genes related to DNA replication. These cell lines are able to induce p21 expression upon Ki-67 depletion. On the contrary, alteration of transcription and cell cycle progression were not observed in tumor-derived HeLa, U2OS and 293T cell lines. These cell lines do not induce p21 expression either. I additionally examined the Ki-67 function in mouse cell cultures. Depletion of Ki-67 neither redistributes inactive X chromosome nor regulates S phase progression in primary female mouse embryonic cells