Entanglement witnesses and geometry of entanglement of two--qutrit states

We construct entanglement witnesses with regard to the geometric structure of the Hilbert--Schmidt space and investigate the geometry of entanglement. In particular, for a two--parameter family of two--qutrit states that are part of the magic simplex we calculate the Hilbert--Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three--parameter family of states. In this way we discover new regions of bound entangled states. Furthermore we outline how to use our method to distinguish entangled from separable states.Comment: 23 pages, 8 figure

Characterizing entanglement with geometric entanglement witnesses

We show how to detect entangled, bound entangled, and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert-Schmidt geometry and can be shifted along parameterized lines. The involved conditions are simplified using Bloch decompositions of operators and states. As an example we determine the three different types of states for a family of two-qutrit states that is part of the "magic simplex", i.e. the set of Bell-state mixtures of arbitrary dimension.Comment: 19 pages, 4 figures, some typos and notational errors corrected. To be published in J. Phys. A: Math. Theo

General Depolarized Pure States: Identification and Properties

The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some multipartite pure states. Here a generalized Schmidt decomposition is given for states which are equivalent to depolarized pure states. Experimental methods for the identification of this class of mixed states are provided and some examples are discussed which show the utility of this description. A particularly interesting example provides, for the first time, an interpretation of the number of negative eigenvalues of the density matrix.Comment: 1 figure, 9 pages, revtex4, slightly rewritten, reorganized, new sectio

Homogeneous Open Quantum Random Walks on a lattice

We study Open Quantum Random Walks for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. We consider the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process, and an ergodic result for the state process. We study in detail the case of homogeneous OQRWs on a lattice, with internal space $h={\mathbb C}^2$

A partial ordering of sets, making mean entropy monotone

Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of subsystems. The entropy per unit volume or unit weight, the mean entropy, is then decreasing with respect to an order relation of the subsystems, defined in this paper. In the context of statistical mechanics a lattice system is studied in detail, and a decrease of mean energy is deduced for blow-up sequences of regular and irregular octogons.Comment: 20 pages, Latex2e, using \usepackage{a4,amsthm,amsfonts,latexsym,amssymb} \usepackage{curves

Extended O-doped polycyclic aromatic hydrocarbons

The synthesis of O-doped benzorylenes, in which peripheral carbon atoms have been replaced by oxygen atoms, has been achieved for the first time. This includes key high-yielding ring-closure steps which, through intramolecular C−O bond formation, allow stepwise planarization of oligonaphthalenes. Single-crystal X-ray diffraction showed that the tetraoxa derivative forms remarkable face-to-face π–π stacks in the solid state, a favorable solid-state arrangement for organic electronics

Predictions versus high-throughput experiments in T-cell epitope discovery: competition or synergy?

Prediction methods as well as experimental methods for T-cell epitope discovery have developed significantly in recent years. High-throughput experimental methods have made it possible to perform full-length protein scans for epitopes restricted to a limited number of MHC alleles. The high costs and limitations regarding the number of proteins and MHC alleles that are feasibly handled by such experimental methods have made in silico prediction models of high interest. MHC binding prediction methods are today of a very high quality and can predict MHC binding peptides with high accuracy. This is possible for a large range of MHC alleles and relevant length of binding peptides. The predictions can easily be performed for complete proteomes of any size. Prediction methods are still, however, dependent on good experimental methods for validation, and should merely be used as a guide for rational epitope discovery. We expect prediction methods as well as experimental validation methods to continue to develop and that we will soon see clinical trials of products whose development has been guided by prediction methods

<i>SNHG5</i> promotes colorectal cancer cell survival by counteracting STAU1-mediated mRNA destabilization

We currently have limited knowledge of the involvement of long non-coding RNAs (lncRNAs) in normal cellular processes and pathologies. Here, we identify and characterize SNHG5 as a stable cytoplasmic lncRNA with up-regulated expression in colorectal cancer. Depletion of SNHG5 induces cell cycle arrest and apoptosis in vitro and limits tumour outgrowth in vivo, whereas SNHG5 overexpression counteracts oxaliplatin-induced apoptosis. Using an unbiased approach, we identify 121 transcript sites interacting with SNHG5 in the cytoplasm. Importantly, knockdown of key SNHG5 target transcripts, including SPATS2, induces apoptosis and thus mimics the effect seen following SNHG5 depletion. Mechanistically, we suggest that SNHG5 stabilizes the target transcripts by blocking their degradation by STAU1. Accordingly, depletion of STAU1 rescues the apoptosis induced after SNHG5 knockdown. Hence, we characterize SNHG5 as a lncRNA promoting tumour cell survival in colorectal cancer and delineate a novel mechanism in which a cytoplasmic lncRNA functions through blocking the action of STAU1

Asymptotic properties of quantum Markov chains

The asymptotic dynamics of quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space on which the resulting quantum Markov chain is diagonalizable. A construction procedure of a basis of this attractor space and its associated dual basis is presented. It applies whenever a strictly positive quantum state exists which is contracted or left invariant by the generating quantum operation. Moreover, algebraic relations between the attractor space and Kraus operators involved in the definition of a quantum Markov chain are derived. This construction is not only expected to offer significant computational advantages in cases in which the dimension of the Hilbert space is large and the dimension of the attractor space is small but it also sheds new light onto the relation between the asymptotic dynamics of quantum Markov chains and fixed points of their generating quantum operations.Comment: 10 page

Entanglement is a costly life-history stage in large whales

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ecology and Evolution 7 (2017): 92–106, doi:10.1002/ece3.2615.Individuals store energy to balance deficits in natural cycles; however, unnatural events can also lead to unbalanced energy budgets. Entanglement in fishing gear is one example of an unnatural but relatively common circumstance that imposes energetic demands of a similar order of magnitude and duration of life-history events such as migration and pregnancy in large whales. We present two complementary bioenergetic approaches to estimate the energy associated with entanglement in North Atlantic right whales, and compare these estimates to the natural energetic life history of individual whales. Differences in measured blubber thicknesses and estimated blubber volumes between normal and entangled, emaciated whales indicate between 7.4 × 1010 J and 1.2 × 1011 J of energy are consumed during the course to death of a lethal entanglement. Increased thrust power requirements to overcome drag forces suggest that when entangled, whales require 3.95 × 109 to 4.08 × 1010 J more energy to swim. Individuals who died from their entanglements performed significantly more work (energy expenditure × time) than those that survived; entanglement duration is therefore critical in determining whales’ survival. Significant sublethal energetic impacts also occur, especially in reproductive females. Drag from fishing gear contributes up to 8% of the 4-year female reproductive energy budget, delaying time of energetic equilibrium (to restore energy lost by a particular entanglement) for reproduction by months to years. In certain populations, chronic entanglement in fishing gear can be viewed as a costly unnatural life-history stage, rather than a rare or short-term incident.Cooperative Institute for the North Atlantic Region (CINAR) Grant Number: NA14OAR4320158; Herrington-Fitch Family Foundation; M.S. Worthington Foundation; North Pond Foundation; Natural Sciences and Engineering Research Council of Canada; MIT Martin Family for Sustainability Fellowshi