Random quantum channels I: graphical calculus and the Bell state phenomenon

This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a random quantum channel. As an application, we study variations of random matrix models introduced by Hayden \cite{hayden}, and show that their eigenvalues converge almost surely. In particular we obtain for some models sharp improvements on the value of the largest eigenvalue, and this is shown in a further work to have new applications to minimal output entropy inequalities.Comment: Several typos were correcte

Valorificarea reziduului vegetal de seminţe de struguri rezultat din procesele extractive ale compuşilor fenolici

The stepwise extraction process of phenolic compounds from grape seeds ultimately leads to the production of a residue rich in protein, cellulose and substances without nitrogen which can be biodegraded in nature by microorganisms from the soil. The purpose of this research was to verify whether the vegetable residue of grape seeds, resulting from the extraction of polymerized proanthocyanidins can be used as an organic fertilizer in the soil. The soil biodegradation process was assessed by microbiological analysis and analysis of current and potential dehydrogenase activity. The results obtained showed that the vegetal residue led to the increaseof the number of soil microorganisms involved in the nitrogen circuit and carbon, as a result of the triggering of the biodegradation process as well as its non-polluting effect supported by current and potential dehydrogenase activity determined in dynamicsover a year in experimental plots

Activitatea antimicrobiană a unui bioprodus biologic activ obţinut din seminţele de struguri

At the Research Station for Viticulture and Enology Iasi, a polymeric condensed proanthocyanidins was obtained from Fetească neagră grape seeds, through a phase preparation, which under determined conditions with hydrogen peroxide, led to the production of a water-soluble bio product with antibacterial, antifungal and antioxidant properties. Evaluation of the antimicrobial activity of the bio product was performed by determining minimum inhibitory concentration (MIC) and minimal bactericidal concentration (CMB) against Staphylococcus aureus and Escherichia coli. From the analysis of the obtained data it was found that the bio product reacted differently from the tested species, being more active against Staphylococcus aureus (G +). The determined MIC was 1.5 mg/mL and the CMB 2.0 mg / mL. In the case of the Escherichia coli (G-) test, the MIC and CMB values were equal but increased to 3.0 mg/mL

A Search for New Galactic Magnetars in Archival Chandra and XMM-Newton Observations

We present constraints on the number of Galactic magnetars, which we have established by searching for sources with periodic variability in 506 archival Chandra observations and 441 archival XMM-Newton observations of the Galactic plane (|b|<5 degree). Our search revealed four sources with periodic variability on time scales of 200-5000 s, all of which are probably accreting white dwarfs. We identify 7 of 12 known Galactic magnetars, but find no new examples with periods between 5 and 20 s. We convert this non-detection into limits on the total number of Galactic magnetars by computing the fraction of the young Galactic stellar population that was included in our survey. We find that easily-detectable magnetars, modeled after persistent anomalous X-ray pulsars, could have been identified in 5% of the Galactic spiral arms by mass. If we assume there are 3 previously-known examples within our random survey, then there are 59 (+92,-32) in the Galaxy. Transient magnetars in quiescence could have been identified throughout 0.4% of the spiral arms, and the lack of new examples implies that <540 exist in the Galaxy (90% confidence). Similar constraints are found by considering the detectability of transient magnetars in outburst by current and past X-ray missions. For assumed lifetimes of 1e4 yr, we find that the birth rate of magnetars could range between 0.003 and 0.06 per year. Therefore, the birth rate of magnetars is at least 10% of that for normal radio pulsars. The magnetar birth rate could exceed that of radio pulsars, unless the lifetimes of transient magnetars are >1e5 yr. Obtaining better constraints will require wide-field X-ray or radio searches for transient X-ray pulsars similar to XTE J1810--197, AX J1845.0--0250, CXOU J164710.2--455216, and 1E 1547.0-5408.Comment: 16 pages, 10 figures, one with a bit of color. submitted to Ap

Random graph states, maximal flow and Fuss-Catalan distributions

For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated to a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by these novel distributions of eigenvalues.Comment: 37 pages, 24 figure

Random matrix techniques in quantum information theory

The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review, combined with more detailed examples -- coming from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels

Radical heminephrectomy for left sided upper pole renal tumor on horseshoe kidney – case report and review of the literature

Ion Chiricuţă Oncological Institute Cluj Napoca, Al V-lea Congres de Urologie, Dializă şi Transplant Renal din Republica Moldova cu participare internaţională (1-13 iunie 2011)Abstract Tumoral pathology of the horseshoe kidney is a rare pathology, only half of the tumors represent renal cell carcinoma. We will present the case of a 45 year old man known with horseshoe kidney diagnosed with a large renal tumor on the left side. CT angiography was performed preoperatively to asses the vascular anomalies of the renal pedicle and it was used for planning the surgical approach. The approach was transperitoneal by subcostal incision with lateral paramedian extension

Random repeated quantum interactions and random invariant states

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}

Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product

Given two positive integers $n$ and $k$ and a parameter $t\in (0,1)$, we choose at random a vector subspace $V_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n}$ of dimension $N\sim tnk$. We show that the set of $k$-tuples of singular values of all unit vectors in $V_n$ fills asymptotically (as $n$ tends to infinity) a deterministic convex set $K_{k,t}$ that we describe using a new norm in $\R^k$. Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result result comes together with a law of large numbers for the singular value decomposition of the eigenvectors corresponding to large eigenvalues of a random truncation of a matrix with high eigenvalue degeneracy.Comment: v3 changes: minor typographic improvements; accepted versio