Minimal qubit tomography

We present, and analyze thoroughly, a highly symmetric and efficient scheme for the determination of a single-qubit state, such as the polarization properties of photons emitted by a single-photon source. In our scheme there are only four measured probabilities, just enough for the determination of the three parameters that specify the qubit state, whereas the standard procedure would measure six probabilities.Comment: 14 pages, 10 figures; final versio

Acquired heart block: A possible complication of patent ductus arteriosus in a preterm infant

A large patent ductus arteriosus (PDA) is a frequently encountered clinical problem in extremely low birth weight (ELBW) infants. It leads to an increased pulmonary blood flow and in a decreased or reversed diastolic flow in the systemic circulation, resulting in complications. Here we report a possible complication of PDA not previously published. On day 8 of life, a male ELBW infant (birth weight 650 g) born at a gestational age of 23 weeks and 3 days developed an atrioventricular block (AV block). The heart rate dropped from 168/min to 90/min, and the ECG showed a Wenckebach second-degree AV block and intraventricular conduction disturbances. Echocardiography demonstrated a PDA with a large left-to-right shunt and large left atrium and left ventricle with high contractility. Within several minutes after surgical closure of the PDA, the heart rate increased, and after 30 min the AV block had improved to a 1: 1 conduction ratio. Echocardiography after 2 h revealed a significant decrease of the left ventricular and atrial dimensions. Within 12 h, the AV block completely reversed together with the intraventricular conduction disturbances. We suggest that PDA with a large left-to-right shunt and left ventricular volume overload may lead to an AV block in an ELBW infant. Surgical closure of the PDA may be indicated. Copyright (C) 2007 S. Karger AG, Basel

Raman-modes of index-identified free-standing single-walled carbon nanotubes

Using electron diffraction on free-standing single-walled carbon nanotubes we have determined the structural indices (n,m) of tubes in the diameter range from 1.4 to 3nm. On the same free-standing tubes we have recorded Raman spectra of the tangential modes and the radial breathing mode. For the smaller diameters (1.4-1.7nm) these measurements confirm previously established radial breathing mode frequency versus diameter relations, and would be consistent with the theoretically predicted proportionality to the inverse diameter. However, for extending the relation to larger diameters, either a yet unexplained environmental constant has to be assumed, or the linear relation has to be abandoned.Comment: 4 pages, 4 figures, +additional materials (select PostScript to obtain it

Minimax mean estimator for the trine

We explore the question of state estimation for a qubit restricted to the $x$-$z$ plane of the Bloch sphere, with the trine measurement. In our earlier work [H. K. Ng and B.-G. Englert, eprint arXiv:1202.5136[quant-ph] (2012)], similarities between quantum tomography and the tomography of a classical die motivated us to apply a simple modification of the classical estimator for use in the quantum problem. This worked very well. In this article, we adapt a different aspect of the classical estimator to the quantum problem. In particular, we investigate the mean estimator, where the mean is taken with a weight function identical to that in the classical estimator but now with quantum constraints imposed. Among such mean estimators, we choose an optimal one with the smallest worst-case error-the minimax mean estimator-and compare its performance with that of other estimators. Despite the natural generalization of the classical approach, this minimax mean estimator does not work as well as one might expect from the analogous performance in the classical problem. While it outperforms the often-used maximum-likelihood estimator in having a smaller worst-case error, the advantage is not significant enough to justify the more complicated procedure required to construct it. The much simpler adapted estimator introduced in our earlier work is still more effective. Our previous work emphasized the similarities between classical and quantum state estimation; in contrast, this paper highlights how intuition gained from classical problems can sometimes fail in the quantum arena.Comment: 18 pages, 3 figure

More on coupling coefficients for the most degenerate representations of SO(n)

We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for the most degenerate representation of SO(n), is discussed in detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and Discussion, References adde

How to measure patent thickets – a novel approach

The existing literature identifies patent thickets indirectly. In this paper we propose a novel measure based on patent citations which allows us to measure the density of patent thickets directly. We discuss the algorithm which generates the measure and present descriptive results validating it. Moreover, we identify technology areas which are particularly impacted by patent thickets

Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules

Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape

Simple model for 1/f noise

We present a simple stochastic mechanism which generates pulse trains exhibiting a power law distribution of the pulse intervals and a $1/f^\alpha$ power spectrum over several decades at low frequencies with $\alpha$ close to one. The essential ingredient of our model is a fluctuating threshold which performs a Brownian motion. Whenever an increasing potential $V(t)$ hits the threshold, $V(t)$ is reset to the origin and a pulse is emitted. We show that if $V(t)$ increases linearly in time, the pulse intervals can be approximated by a random walk with multiplicative noise. Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of $1/f^\alpha$ noise observed in cortical neurons and earthquake data.Comment: 4 pages, 4 figure

Symmetric coupling of four spin-1/2 systems

We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.Comment: 20 pages, no figure