Additivity of the Renyi entropy of order 2 for positive-partial-transpose-inducing channels

We prove that the minimal Renyi entropy of order 2 (RE2) output of a positive-partial-transpose(PPT)-inducing channel joint to an arbitrary other channel is equal to the sum of the minimal RE2 output of the individual channels. PPT-inducing channels are channels with a Choi matrix which is bound entangled or separable. The techniques used can be easily recycled to prove additivity for some non-PPT-inducing channels such as the depolarizing and transpose depolarizing channels, though not all known additive channels. We explicitly make the calculations for generalized Werner-Holevo channels as an example of both the scope and limitations of our techniques.Comment: 4 page

A de Finetti representation for finite symmetric quantum states

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.Comment: 22 pages, LaTe

NOVEL FUNCTIONAL HYDROPHILIC POLYMERS AND HYDROGELS FOR MICROANALYTICAL SYSTEMS

This thesis focuses on the use of hydrophilic polymers for bioanalytical applications, including several microanalytical techniques encompassing nanotechnology, microarray technology and DNA gel electrophoresis. The dissertation is divided in two parts, which share the employment of dimethylacrylamide-based copolymers, developed at the laboratory of Analytical Microsystems of the Institute of Chemistry for Molecular Recognition (National Research Council of Italy) where the thesis has been carried out. PART A introduces a novel approach for surface modification of quantum dots and gold nanoparticles, based on physi-/chemisorption of two different functional dimethylacrylamide copolymers. Beside developing innovative functionalization strategies, the goal is to demonstrate the application of coated nanoparticles in highly sensitive immunoassays based on microarray technology. PART B of the dissertation presents the results of an activity, conducted in collaboration with the company Agilent Technology (UK), aimed at developing an innovative gel sieving matrix for high performance DNA electrophoresis. We introduce a new hydrogel obtained by cross-linking an alkyne modified polymer with an azide one, exploiting a copper catalysed click chemistry reaction. The alkyne functionalized polymer is based on poly(dimethilacrylamide) and it was obtained by a post-polymerization modification approach from the parent copolymer poly(DMA-NAS-MAPS), extensively used in the first part of this dissertation. The azide polymer is a polyethylenglycol terminated with azide groups at both ends, and is commercially available. A considerable part of this work is devoted to the optimization of the characteristics of the new hydrogel, in particular to the extension of its shelf-life, an important parameter in view of its industrial application

A de Finetti representation theorem for infinite dimensional quantum systems and applications to quantum cryptography

According to the quantum de Finetti theorem, if the state of an N-partite system is invariant under permutations of the subsystems then it can be approximated by a state where almost all subsystems are identical copies of each other, provided N is sufficiently large compared to the dimension of the subsystems. The de Finetti theorem has various applications in physics and information theory, where it is for instance used to prove the security of quantum cryptographic schemes. Here, we extend de Finetti's theorem, showing that the approximation also holds for infinite dimensional systems, as long as the state satisfies certain experimentally verifiable conditions. This is relevant for applications such as quantum key distribution (QKD), where it is often hard - or even impossible - to bound the dimension of the information carriers (which may be corrupted by an adversary). In particular, our result can be applied to prove the security of QKD based on weak coherent states or Gaussian states against general attacks.Comment: 11 pages, LaTe

When do generalized entropies apply? How phase space volume determines entropy

We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a {\em generalized} (non-additive) form. We show that generalized entropies can only exist when the dynamically (statistically) relevant fraction of degrees of freedom in the system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen and is practically statistically inactive. Systems governed by generalized entropies are therefore systems whose phase space volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for binomial processes and argue that generalized entropies could be relevant for self organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.Comment: 5 pages, 2 figure

Cooperation between Prostaglandin E2 and Epidermal Growth Factor Receptor in Cancer Progression: A Dual Target for Cancer Therapy

It is recognized that prostaglandin E2 (PGE2) is one key lipid mediator involved in chronic inflammation, and it is directly implicated in tumor development by regulating cancer cell growth and migration, apoptosis, epithelial–mesenchymal transition, angiogenesis, and immune escape. In addition, the expression of the enzymes involved in PGE2 synthesis, cyclooxygenase 2 (COX-2) and microsomal prostaglandin E synthase 1 (mPGES1), positively correlates with tumor progression and aggressiveness, clearly indicating the crucial role of the entire pathway in cancer. Moreover, several lines of evidence suggest that the COX2/mPGES1/PGE2 inflammatory axis is involved in the modulation of epidermal growth factor receptor (EGFR) signaling to reinforce the oncogenic drive of EGFR activation. Similarly, EGFR activation promotes the induction of COX2/mPGES1 expression and PGE2 production. In this review, we describe the interplay between COX2/mPGES1/PGE2 and EGFR in cancer, and new therapeutic strategies that target this signaling pathway, to outline the importance of the modulation of the inflammatory process in cancer fighting. © 2023 by the authors

Finite size mean-field models

We characterize the two-site marginals of exchangeable states of a system of quantum spins in terms of a simple positivity condition. This result is used in two applications. We first show that the distance between two-site marginals of permutation invariant states on N spins and exchangeable states is of order 1/N. The second application relates the mean ground state energy of a mean-field model of composite spins interacting through a product pair interaction with the mean ground state energies of the components.Comment: 20 page

Dbl oncogene expression in MCF-10 A epithelial cells disrupts mammary acinar architecture, induces EMT and angiogenic factor secretion.

The proteins of the Dbl family are guanine nucleotide exchange factors (GEFs) of Rho GTPases and are known to be involved in cell growth regulation. Alterations of the normal function of these proteins lead to pathological processes such as developmental disorders, neoplastic transformation, and tumor metastasis. We have previously demonstrated that expression of Dbl oncogene in lens epithelial cells modulates genes encoding proteins involved in epithelial-mesenchymal-transition (EMT) and induces angiogenesis in the lens. Our present study was undertaken to investigate the role of Dbl oncogene in epithelial cells transformation, providing new insights into carcinoma progression. To assess how Dbl oncogene can modulate EMT, cell migration, morphogenesis, and expression of pro-apoptotic and angiogenic factors we utilized bi- and three-dimensional cultures of MCF-10░A cells. We show that upon Dbl expression MCF-10░A cells undergo EMT. In addition, we found that Dbl overexpression sustain

The small GTPase Rab29 is a common regulator of immune synapse assembly and ciliogenesis

Acknowledgements We wish to thank Jorge Galán, Gregory Pazour, Derek Toomre, Giuliano Callaini, Joel Rosenbaum, Alessandra Boletta and Francesco Blasi for generously providing reagents and for productive discussions, and Sonia Grassini for technical assistance. The work was carried out with the financial support of Telethon (GGP11021) and AIRC.Peer reviewedPostprin