Destructive Impact of Molecular Noise on Nanoscale Electrochemical Oscillators

We study the loss of coherence of electrochemical oscillations on meso- and nanosized electrodes with numeric simulations of the electrochemical master equation for a prototypical electrochemical oscillator, the hydrogen peroxide reduction on Pt electrodes in the presence of halides. On nanoelectrodes, the electrode potential changes whenever a stochastic electron-transfer event takes place. Electrochemical reaction rate coefficients depend exponentially on the electrode potential and become thus fluctuating quantities as well. Therefore, also the transition rates between system states become time-dependent which constitutes a fundamental difference to purely chemical nanoscale oscillators. Three implications are demonstrated: (a) oscillations and steady states shift in phase space with decreasing system size, thereby also decreasing considerably the oscillating parameter regions; (b) the minimal number of molecules necessary to support correlated oscillations is more than 10 times as large as for nanoscale chemical oscillators; (c) the relation between correlation time and variance of the period of the oscillations predicted for chemical oscillators in the weak noise limit is only fulfilled in a very restricted parameter range for the electrochemical nano-oscillator.Comment: 18 pages, 9 figure

Intima-Media Thickness: Setting a Standard for a Completely Automated Method of Ultrasound Measurement

The intima - media thickness (IMT) of the common carotid artery is a widely used clinical marker of severe cardiovascular diseases. IMT is usually manually measured on longitudinal B-Mode ultrasound images. Many computer-based techniques for IMT measurement have been proposed to overcome the limits of manual segmentation. Most of these, however, require a certain degree of user interaction. In this paper we describe a new completely automated layers extraction (CALEXia) technique for the segmentation and IMT measurement of carotid wall in ultrasound images. CALEXia is based on an integrated approach consisting of feature extraction, line fitting, and classification that enables the automated tracing of the carotid adventitial walls. IMT is then measured by relying on a fuzzy K-means classifier. We tested CALEXia on a database of 200 images. We compared CALEXia performances to those of a previously developed methodology that was based on signal analysis (CULEXsa). Three trained operators manually segmented the images and the average profiles were considered as the ground truth. The average error from CALEXia for lumen - intima (LI) and media - adventitia (MA) interface tracings were 1.46 ± 1.51 pixel (0.091 ± 0.093 mm) and 0.40 ± 0.87 pixel (0.025 ± 0.055 mm), respectively. The corresponding errors for CULEXsa were 0.55 ± 0.51 pixels (0.035 ± 0.032 mm) and 0.59 ± 0.46 pixels (0.037 ± 0.029 mm). The IMT measurement error was equal to 0.87 ± 0.56 pixel (0.054 ± 0.035 mm) for CALEXia and 0.12 ± 0.14 pixel (0.01 ± 0.01 mm) for CULEXsa. Thus, CALEXia showed limited performance in segmenting the LI interface, but outperformed CULEXsa in the MA interface and in the number of images correctly processed (10 for CALEXia and 16 for CULEXsa). Based on two complementary strategies, we anticipate fusing them for further IMT improvement

Universal quantum magnetometry with spin states at equilibrium

We address metrological protocols for the estimation of the intensity and the orientation of a magnetic field, and show that quantum-enhanced precision may be achieved by probing the field with an arbitrary spin at thermal equilibrium. We derive a general expression for the ultimate achievable precision, as given by the quantum Fisher information, and express this quantity in terms of common thermodynamic quantities. We also seek for the optimal observable, and show that it corresponds to the spin projection along a suitable direction, defined by a universal function of the spin temperature. Finally, we prove the robustness of our scheme against deviations of the measured spin projection from optimality.Comment: Phys. Rev. Lett., in pres

Entanglement entropy and the determination of an unknown quantum state

An initial unknown quantum state can be determined with a single measurement apparatus by letting it interact with an auxiliary, "Ancilla", system as proposed by Allahverdyan, Balian and Nieuwenhuizen [Phys. Rev. Lett. 92, 120402 (2004)]. In the case of two qubits, this procedure allows to reconstruct the initial state of the qubit of interest S by measuring three commuting observables and therefore by means of a single apparatus, for the total system S + A at a later time. The determinant of the matrix of the linear transformation connecting the measurements of three commuting observables at time t > 0 to the components of the polarization vector of S at time t = 0 is used as an indicator of the reconstructability of the initial state of the system S. We show that a connection between the entanglement entropy of the total system S + A and such a determinant exists, and that for a pure state a vanishing entanglement individuates, without a need for any measurement, those intervals of time for which the reconstruction procedure is least efficient. This property remains valid for a generic dimension of S. In the case of a mixed state this connection is lost.Comment: 5 pages 2 figures, accepted for publication on Physical Review