Balanced Tripartite Entanglement, the Alternating Group A4 and the Lie Algebra sl(3,C)⊕u(1)sl(3,C) \oplus u(1)

We discuss three important classes of three-qubit entangled states and their encoding into quantum gates, finite groups and Lie algebras. States of the GHZ and W-type correspond to pure tripartite and bipartite entanglement, respectively. We introduce another generic class B of three-qubit states, that have balanced entanglement over two and three parties. We show how to realize the largest cristallographic group $W(E_8)$ in terms of three-qubit gates (with real entries) encoding states of type GHZ or W [M. Planat, {\it Clifford group dipoles and the enactment of Weyl/Coxeter group $W(E_8)$ by entangling gates}, Preprint 0904.3691 (quant-ph)]. Then, we describe a peculiar "condensation" of $W(E_8)$ into the four-letter alternating group $A_4$, obtained from a chain of maximal subgroups. Group $A_4$ is realized from two B-type generators and found to correspond to the Lie algebra $sl(3,\mathbb{C})\oplus u(1)$. Possible applications of our findings to particle physics and the structure of genetic code are also mentioned.Comment: 14 page

Unexpected Learning: Development of the CoP and Its Members #generational-shift

Our research explores how multigenerational CoPs may provide graduate students, particularly doctoral students, the space to explore and develop their professional identities and find their scholarly voices

Uniqueness of radial solutions for the fractional Laplacian

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian $(-\Delta)^s$ with $s \in (0,1)$ for any space dimensions $N \geq 1$. By extending a monotonicity formula found by Cabre and Sire \cite{CaSi-10}, we show that the linear equation $(-\Delta)^s u+ Vu = 0$ in $\mathbb{R}^N$ has at most one radial and bounded solution vanishing at infinity, provided that the potential $V$ is a radial and non-decreasing. In particular, this result implies that all radial eigenvalues of the corresponding fractional Schr\"odinger operator $H=(-\Delta)^s + V$ are simple. Furthermore, by combining these findings on linear equations with topological bounds for a related problem on the upper half-space $\mathbb{R}^{N+1}_+$, we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation $(-\Delta)^s Q + Q - |Q|^{\alpha} Q = 0$ in $\mathbb{R}^N$ for arbitrary space dimensions $N \geq 1$ and all admissible exponents $\alpha >0$. This generalizes the nondegeneracy and uniqueness result for dimension N=1 recently obtained by the first two authors in \cite{FrLe-10} and, in particular, the uniqueness result for solitary waves of the Benjamin--Ono equation found by Amick and Toland \cite{AmTo-91}.Comment: 38 pages; revised version; various typos corrected; proof of Lemma 8.1 corrected; discussion of case \kappa_* =1 in the proof of Theorem 2 corrected with new Lemma A.2; accepted for publication in Comm. Pure. Appl. Mat

The effect of aging and cardiorespiratory fitness on the lung diffusing capacity response to exercise in healthy humans

Aging is associated with deterioration in the structure and function of the pulmonary circulation. We characterized the lung diffusing capacity for carbon monoxide (DLCO), alveolar-capillary membrane conductance (Dm(CO)), and pulmonary-capillary blood volume (V(C)) response to discontinuous incremental exercise at 25, 50, 75, and 90% of peak work (Wpeak) in four groups: 1) Young [27 ± 3 y, maximal oxygen consumption (V̇O₂max) 110 ± 18% age-predicted]; 2) Young Highly-Fit (27 ± 3 y, V̇O₂max 147 ± 8% age-predicted); 3) Old (69 ± 5 y, V̇O₂max 116 ± 13% age-predicted); and 4) Old Highly-Fit (65 ± 5 y, V̇O₂max 162 ± 18% age-predicted). At rest and at 90% Wpeak, DLCO, Dm(CO), and VC were decreased with age. At 90% Wpeak, DLCO, Dm(CO) and VC were greater in Old Highly-Fit vs. Old adults. The slope of the DLCO-cardiac output (Q̇) relationship from rest to end-exercise at 90% Wpeak was not different between Young, Young Highly-Fit, Old and Old Highly-Fit (1.35 vs. 1.44 vs. 1.10 vs. 1.35 mlCO·mmHg⁻¹·Lblood⁻¹, P = 0.388), with no evidence of a plateau in this relationship during exercise; this was also true for Dm(CO)-Q̇ and V(C)-Q̇. V̇O2max was positively correlated with: 1) DLCO, Dm(CO), and V(C) at rest; 2) the rest to end-exercise change in DLCO, Dm(CO), and V(C). In conclusion, these data suggest that despite the age-associated deterioration in the structure and function of the pulmonary circulation, expansion of the pulmonary capillary network does not become limited during exercise in healthy individuals regardless of age or cardiorespiratory fitness level

Bounds of concurrence and their relation with fidelity and frontier states

The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a given value of concurrence, the states achieving the maximal upper bound, the minimal lower bound or the maximal difference upper-lower bound are determined analytically

Heparanase deglycanation of syndecan-1 is required for binding of the epithelial-restricted prosecretory mitogen lacritin

Cell surface heparan sulfate (HS) proteoglycans are carbohydrate-rich regulators of cell migratory, mitogenic, secretory, and inflammatory activity that bind and present soluble heparin-binding growth factors (e.g., fibroblast growth factor, Wnt, Hh, transforming growth factor β, amphiregulin, and hepatocyte growth factor) to their respective signaling receptors. We demonstrate that the deglycanated core protein of syndecan-1 (SDC1) and not HS chains nor SDC2 or -4, appears to target the epithelial selective prosecretory mitogen lacritin. An important and novel step in this mechanism is that binding necessitates prior partial or complete removal of HS chains by endogenous heparanase. This limits lacritin activity to sites where heparanase appears to predominate, such as sites of exocrine cell migration, secretion, renewal, and inflammation. Binding is mutually specified by lacritin's C-terminal mitogenic domain and SDC1's N terminus. Heparanase modification of the latter transforms a widely expressed HS proteoglycan into a highly selective surface-binding protein. This novel example of cell specification through extracellular modification of an HS proteoglycan has broad implications in development, homeostasis, and disease

Heralded generation of entangled photon pairs

Entangled photons are a crucial resource for quantum communication and linear optical quantum computation. Unfortunately, the applicability of many photon-based schemes is limited due to the stochastic character of the photon sources. Therefore, a worldwide effort has focused in overcoming the limitation of probabilistic emission by generating two-photon entangled states conditioned on the detection of auxiliary photons. Here we present the first heralded generation of photon states that are maximally entangled in polarization with linear optics and standard photon detection from spontaneous parametric down-conversion. We utilize the down-conversion state corresponding to the generation of three photon pairs, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state. This controlled generation of entangled photon states is a significant step towards the applicability of a linear optics quantum network, in particular for entanglement swapping, quantum teleportation, quantum cryptography and scalable approaches towards photonics-based quantum computing

An apoferritin-based drug delivery system for the tyrosine kinase inhibitor gefitinib

Anticancer drug Gefitinib encapsulated within human heavy chain apoferritin by diffusion allows pH-controlled sustained release of cargo. The combination of increased cellular uptake, and potent and enhanced antitumor activity against the HER2 overexpressing SKBR3 cell line compared to Gefitinib alone, makes it a promising carrier for delivery of drugs to tumor sites. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Experimental delayed-choice entanglement swapping

Motivated by the question, which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayed-choice entanglement swapping. There, entanglement can be "produced a posteriori, after the entangled particles have been measured and may no longer exist". In this work we report the first realization of Peres' gedanken experiment. Using four photons, we can actively delay the choice of measurement-implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator-on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as "quantum steering into the past"

Detection of multipartite entanglement with two-body correlations

We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our criteria can straightforwardly be applied for detecting different forms of multipartite entanglement in familiar spin models in thermal equilibrium.Comment: 5 pages including 2 figures, LaTeX; for the proceedings of the DPG spring meeting, Berlin, March 200