Adaptive homodyne measurement of optical phase

We present an experimental demonstration of the power of feedback in quantum metrology, confirming the predicted [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)]] superior performance of an adaptive homodyne technique for single-shot measurement of optical phase. For measurements performed on weak coherent states with no prior knowledge of the signal phase, adaptive homodyne estimation approaches closer to the intrinsic quantum uncertainty than any previous technique. Our results underscore the importance of real-time feedback for reaching quantum limits in measurement and control.     

Entropy of Hidden Markov Processes via Cycle Expansion

Hidden Markov Processes (HMP) is one of the basic tools of the modern probabilistic modeling. The characterization of their entropy remains however an open problem. Here the entropy of HMP is calculated via the cycle expansion of the zeta-function, a method adopted from the theory of dynamical systems. For a class of HMP this method produces exact results both for the entropy and the moment-generating function. The latter allows to estimate, via the Chernoff bound, the probabilities of large deviations for the HMP. More generally, the method offers a representation of the moment-generating function and of the entropy via convergent series.     

On Path Factors of (3, 4)-Biregular Bigraphs

A (3, 4)-biregular bigraph G is a bipartite graph where all vertices in one part have degree 3 and all vertices in the other part have degree 4. A path factor of G is a spanning subgraph whose components are nontrivial paths. We prove that a simple (3,4)-biregular bigraph always has a path factor such that the endpoints of each path have degree three. Moreover we suggest a polynomial algorithm for the construction of such a path factor.     

New Local Conditions for a Graph to be Hamiltonian

For a vertex w of a graph G the ball of radius 2 centered at w is the subgraph of G induced by the set M₂(w) of all vertices whose distance from w does not exceed 2. We prove the following theorem: Let G be a connected graph where every ball of radius 2 is 2-connected and d(u)+d(v)≥|M₂(w)|−1 for every induced path uwv. Then either G is hamiltonian or for some p≥2 where ∨ denotes join. As a corollary we obtain the following local analogue of a theorem of Nash-Williams: A connected r-regular graph G is hamiltonian if every ball of radius 2 is 2-connected and for each vertex w of G. Supported by the Swedish Research Council (VR)     

Solid-phase synthesis of trisubsituted guanidines

The solid-phase library synthesis of trisubstituted guanidines was accomplished. Amines were loaded onto the 4-formyl-3,5-dimethoxyphenoxymethyl linker via reductive amination. Subsequent acylation with Fmoc-4-aminomethylbenzoic acid followed by Fmoc deprotection gave solid-supported primary amines. Alternatively, sulfonylation of resin-bound secondary amines with 4-cyanobenzenesulfonyl chloride followed by borane reduction also gave solid-supported primary amines. Both resins were acylated with isocyanates to furnish solid-supported ureas. Dehydration of ureas with p-toluenesulfonyl chloride in pyridine gave solid-supported carbodiimides. Nucleophilic addition of amines to the carbodiimide bond followed by cleavage off the solid support gave trisubstituted guanidines.     

Comparison of methods for extraction of ethyl carbamate from alcoholic beverages in gas chromatography/mass spectrometry analysis

A procedure to analyze ethyl carbamate (EC) by gas chromatography/mass spectrometry was optimized and validated. Deuterated EC (d5-EC) was added to the samples as an internal standard followed by extraction with polystyrene crosslinked polystyrene cartridges using minimal volumes of ethyl acetate. The EC response was measured in selective ion monitoring (SIM) mode and found to be linear in the range between the limit of quantitation (10 micro/L) and 1000 microg/L. EC recoveries varied from 92 to 112%, with the average value of 100 +/- 8%. The procedure compared well (r2 = 0.9970) with the existing AOAC Official Method with the added benefits of minimal solvent usage and reduced matrix interferences.     

Total synthesis of (+)-pinnatoxin A

A convergent enantioselective total synthesis of (+)-pinnatoxin A is described. The synthesis capitalizes on the highly diastereoselective Ireland-Claisen rearrangement of an acyclic alpha-branched allylic ester to set the quaternary stereogenic center at the core of the spiroimine ring system along with the adjacent tertiary stereocenter. The all-carbon macrocyclic ring system was formed by ring-closing metathesis.     

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.