Fully undistillable quantum states are separable

Assume that Alice, Bob, and Eve share a tripartite pure state $|\psi_{ABE}\rangle$. We prove that if Alice cannot distill entanglement with either Bob or Eve using $|\psi_{ABE}\rangle$ and local operations with any one of the following configurations for classical communication: $(A\to B, A\leftrightarrow E), (A\leftrightarrow B, A\to E),$ and $(A\leftrightarrow B, A\leftrightarrow E)$, then the same is also true for the other two configurations. Moreover, this happens precisely when the state is such that both its reductions $\rho_{AB}$ and $\rho_{AE}$ are separable, which is further equivalent to the reductions being PPT. This, in particular, implies that any NPT bipartite state is such that either the state itself or its complement is 2-way distillable. In proving these results, we first obtain an explicit lower bound on the 2-way distillable entanglement of low rank bipartite states. Furthermore, we show that even though not all low rank states are 1-way distillable, a randomly sampled low rank state will almost surely be 1-way distillable

The PPT2^2 conjecture holds for all Choi-type maps

We prove that the PPT$^2$ conjecture holds for linear maps between matrix algebras which are covariant under the action of the diagonal unitary group. Many salient examples, like the Choi-type maps, Classical maps, Schur multipliers, and mixtures thereof, lie in this class. Our proof relies on a generalization of the matrix-theoretic notion of factor width for pairwise completely positive matrices, and a complete characterization in the case of factor width two

Bi-PPT channels are entanglement breaking

In a recent paper, Hirche and Leditzky introduced the notion of bi-PPT channels which are quantum channels that stay completely positive under composition with a transposition and such that the same property holds for one of their complementary channels. They asked whether there are examples of such channels that are not antidegradable. We show that this is not the case, since bi-PPT channels are always entanglement breaking. We also show that degradable quantum channels staying completely positive under composition with a transposition are entanglement breaking

Performance Evaluation of an Independent Time Optimized Infrastructure for Big Data Analytics that Maintains Symmetry

Traditional data analytics tools are designed to deal with the asymmetrical type of data i.e., structured, semi-structured, and unstructured. The diverse behavior of data produced by different sources requires the selection of suitable tools. The restriction of recourses to deal with a huge volume of data is a challenge for these tools, which affects the performances of the tool's execution time. Therefore, in the present paper, we proposed a time optimization model, shares common HDFS (Hadoop Distributed File System) between three Name-node (Master Node), three Data-node, and one Client-node. These nodes work under the DeMilitarized zone (DMZ) to maintain symmetry. Machine learning jobs are explored from an independent platform to realize this model. In the first node (Name-node 1), Mahout is installed with all machine learning libraries through the maven repositories. The second node (Name-node 2), R connected to Hadoop, is running through the shiny-server. Splunk is configured in the third node (Name-node 3) and is used to analyze the logs. Experiments are performed between the proposed and legacy model to evaluate the response time, execution time, and throughput. K-means clustering, Navies Bayes, and recommender algorithms are run on three different data sets, i.e., movie rating, newsgroup, and Spam SMS data set, representing structured, semi-structured, and unstructured data, respectively. The selection of tools defines data independence, e.g., Newsgroup data set to run on Mahout as others cannot be compatible with this data. It is evident from the outcome of the data that the performance of the proposed model establishes the hypothesis that our model overcomes the limitation of the resources of the legacy model. In addition, the proposed model can process any kind of algorithm on different sets of data, which resides in its native formats

Assessing the effect of reclaimed asphalt pavement on the fatigue and healing of flexible pavement materials

The Netherlands has one of the densest road networks with over 140,000 km of roadways. Fatigue cracking is an important distress in flexible pavements. This form of distress results from the application of repeated traffic loading which causes failure. Fatigue cracking assessment on various base layer asphalt mixtures including reclaimed asphalt pavement materials and recycling agents has been addressed in this research work. This research work aims to develop a method for quantifying and assessing this fatigue characterization including the self-healing mechanism of asphalt mixtures using Visco Elastic Continuum Damage Theory. The self-healing in asphalt mixtures was assessed by incorporating group-rest healing periods in a self-developed laboratory testing method. The reliable self-healing models for asphalt mixtures with recycled asphalt materials and recycling agents based on temperature, damage state, and rest periods were predicted using the damage characteristics curve (C-S). Bottom-up cracking in base layer asphalt mixtures was modeled and studied using finite element modeling software FlexPAVE based on the Visco-Elastic Continuum Damage theory. A vivid assessment of mixtures for fatigue and healing characterization is discussed in this research work.This research work is interrelated with an ongoing project, which aims at developing a protocol to determine the shift factors for the fatigue life of asphalt mixtures to correct healing and aging. The project runs under the umbrella of Knowledge-based Pavement Engineering (KPE), a joint program among Rijkswaterstaat, TNO, and TU Delft. Dura Vermeer is contributing partner to this MSc graduation research work as well.Civil Engineering | Structural Engineerin

Diagonal unitary and orthogonal symmetries in quantum theory

International audienceWe analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the literature, which includes notable entries like the Diagonal Symmetric states and the Choi-type maps, we show that this class of matrices (and maps) encompasses a wide variety of scenarios, thereby unifying their study. We examine their linear algebraic structure and investigate different notions of positivity through their convex conic manifestations. In particular, we generalize the well-known cone of completely positive matrices to that of triplewise completely positive matrices and connect it to the separability of the relevant invariant states (or the entanglement breaking property of the corresponding quantum channels). For linear maps, we provide explicit characterizations of the stated covariance in terms of their Kraus, Stinespring, and Choi representations, and systematically analyze the usual properties of positivity, decomposability, complete positivity, and the like. We also describe the invariant subspaces of these maps and use their structure to provide necessary and sufficient conditions for separability of the associated invariant bipartite states

A graphical calculus for integration over random diagonal unitary matrices

International audienceWe provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially ordered set of uniform block permutations. A similar calculus is developed for random vectors consisting of independent uniform signs, based on the combinatorics of the partially ordered set of even partitions. We employ our method to extend some of the results by Johnston and MacLean on the family of local diagonal unitary invariant matrices. Furthermore, our graphical approach applies just as well to the real (orthogonal) case, where we introduce the notion of triplewise complete positivity to study the condition for separability of the relevant bipartite matrices. Finally, we analyze the twirling of linear maps between matrix algebras by independent diagonal unitary matrices, showcasing another application of our method

Nodal Langerhans cell neoplasm: detailing the diagnostic quandaries

Langerhans cells, found in the supra-basal region of the mucous membranes in the epidermis of the skin, in lymph nodes and thymus, function as antigen-presenting cells within the histiocyte system. Tumors derived from Langerhans cells (LC) can be divided according to the degree of cytological atypia and clinical behavior into Langerhans cell histiocytosis (LCH) and Langerhans cell sarcoma (LCS). LCS is rare, and the nodal presentation is even rarer with challenging histological characteristics. LCS has a dismal overcome despite intensive chemotherapy. Herein, we report a case of a 29-year-old male who presented with generalized lymphadenopathy initially considered as a lymphoma. An outright definitive diagnosis could not be attained in the initial histomorphological and immunohistochemical evaluation, fraught with differential diagnoses. The key to decoding the precise neoplasm was a combination of the cytopathologic features, review of the histomorphology, and extensive immunohistochemical assessment in conjunction with the clinical and positron emission tomography (PET) scan findings. The best diagnosis proffered was a Langerhans cell histiocytosis progressing to Langerhans cell sarcoma. This case highlights the grey zone areas in LC neoplasms, the diagnostic conundrums encountered, the indispensable role of meticulous pathological analysis, and the importance of ancillary studies in hammering out the final diagnosis

Ergodic theory of diagonal orthogonal covariant quantum channels

We analyze the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic matrix. This allows us to exploit tools from classical ergodic theory to study quantum ergodicity of such channels. As an application of our analysis, we study dual unitary brickwork circuits which have recently been proposed as minimal models of quantum chaos in many-body systems. Upon imposing a local diagonal orthogonal invariance symmetry on these circuits, the long-term behaviour of spatio-temporal correlations between local observables in such circuits is completely determined by the ergodic properties of a channel that is covariant under diagonal orthogonal transformations. We utilize this fact to show that such symmetric dual unitary circuits exhibit a rich variety of ergodic behaviours, thus emphasizing their importance

Implementation of Retinal Pathways

<p><span>Research in Retinal Pathways has been increasing in recent times. This research opens so many possibilities of analog computation techniques in future. To advance the research in this domain, understanding of mathematical formulation and electrical properties of retinal pathways is necessary. By analysing this formulation, a transistorized design of retinal pathways. Both the mathematical and transistorised model are implemented using MATLAB and LTspice respectively and it works for same input conditions and produces similar output. The transistorized design effectively produces the stimulus from rod and cone cells to ganglion cells..</span></p&gt