High-rate, high-fidelity entanglement of qubits across an elementary quantum network

We demonstrate remote entanglement of trapped-ion qubits via a quantum-optical fiber link with fidelity and rate approaching those of local operations. Two ${}^{88}$Sr${}^{+}$ qubits are entangled via the polarization degree of freedom of two photons which are coupled by high-numerical-aperture lenses into single-mode optical fibers and interfere on a beamsplitter. A novel geometry allows high-efficiency photon collection while maintaining unit fidelity for ion-photon entanglement. We generate remote Bell pairs with fidelity $F=0.940(5)$ at an average rate $182\,\mathrm{s}^{-1}$ (success probability $2.18\times10^{-4}$).Comment: v2 updated to include responses to reviewers, as published in PR

Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

The Supremum Norm of the Discrepancy Function: Recent Results and Connections

A great challenge in the analysis of the discrepancy function D_N is to obtain universal lower bounds on the L-infty norm of D_N in dimensions d \geq 3. It follows from the average case bound of Klaus Roth that the L-infty norm of D_N is at least (log N) ^{(d-1)/2}. It is conjectured that the L-infty bound is significantly larger, but the only definitive result is that of Wolfgang Schmidt in dimension d=2. Partial improvements of the Roth exponent (d-1)/2 in higher dimensions have been established by the authors and Armen Vagharshakyan. We survey these results, the underlying methods, and some of their connections to other subjects in probability, approximation theory, and analysis.Comment: 15 pages, 3 Figures. Reports on talks presented by the authors at the 10th international conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Sydney Australia, February 2011. v2: Comments of the referee are incorporate

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Receptor activity modifying proteins (RAMPs) interact with the VPAC 2 receptor and CRF 1 receptors and modulate their function: RAMP interactions with VPAC2and CRF1receptors

Although it is established that the receptor activity modifying proteins (RAMPs) can interact with a number of GPCRs, little is known about the consequences of these interactions. Here the interaction of RAMPs with the glucagon-like peptide 1 receptor (GLP-1 receptor), the human vasoactive intestinal polypeptide/pituitary AC-activating peptide 2 receptor (VPAC2) and the type 1 corticotrophin releasing factor receptor (CRF1) has been examined

Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems

We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized volume elements of the Bures (minimal monotone) metric for n = 2 and 3, obtaining thereby "Bures prior probability distributions" over the two- and three-state systems. Then, as an essential first step in extending these results to n > 3, we determine that the "Hall normalization constant" (C_{n}) for the marginal Bures prior probability distribution over the (n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known to equal 2/pi.) The constant C_{5} is also found. It too is associated with a remarkably simple decompositon, involving the product of the eight consecutive prime numbers from 2 to 23. We also preliminarily investigate several cases, n > 5, with the use of quasi-Monte Carlo integration. We hope that the various analyses reported will prove useful in deriving a general formula (which evidence suggests will involve the Bernoulli numbers) for the Hall normalization constant for arbitrary n. This would have diverse applications, including quantum inference and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in J. Phys. A. We make a few slight changes from the previous version, but also add a subsection (III G) in which several variations of the basic problem are newly studied. Rather strong evidence is adduced that the Hall constants are related to partial sums of denominators of the even-indexed Bernoulli numbers, although a general formula is still lackin

Performance analysis of priority queueing systems in discrete time

The integration of different types of traffic in packet-based networks spawns the need for traffic differentiation. In this tutorial paper, we present some analytical techniques to tackle discrete-time queueing systems with priority scheduling. We investigate both preemptive (resume and repeat) and non-preemptive priority scheduling disciplines. Two classes of traffic are considered, high-priority and low-priority traffic, which both generate variable-length packets. A probability generating functions approach leads to performance measures such as moments of system contents and packet delays of both classes

Live Imaging of Mitosomes and Hydrogenosomes by HaloTag Technology

Hydrogenosomes and mitosomes represent remarkable mitochondrial adaptations in the anaerobic parasitic protists such as Trichomonas vaginalis and Giardia intestinalis, respectively. In order to provide a tool to study these organelles in the live cells, the HaloTag was fused to G. intestinalis IscU and T. vaginalis frataxin and expressed in the mitosomes and hydrogenosomes, respectively. The incubation of the parasites with the fluorescent Halo-ligand resulted in highly specific organellar labeling, allowing live imaging of the organelles. With the array of available ligands the HaloTag technology offers a new tool to study the dynamics of mitochondria-related compartments as well as other cellular components in these intriguing unicellular eukaryotes