Uncollapsing the wavefunction by undoing quantum measurements

We review and expand on recent advances in theory and experiments concerning the problem of wavefunction uncollapse: Given an unknown state that has been disturbed by a generalized measurement, restore the state to its initial configuration. We describe how this is probabilistically possible with a subsequent measurement that involves erasing the information extracted about the state in the first measurement. The general theory of abstract measurements is discussed, focusing on quantum information aspects of the problem, in addition to investigating a variety of specific physical situations and explicit measurement strategies. Several systems are considered in detail: the quantum double dot charge qubit measured by a quantum point contact (with and without Hamiltonian dynamics), the superconducting phase qubit monitored by a SQUID detector, and an arbitrary number of entangled charge qubits. Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and the optical polarization qubit are also reviewed. For each of these systems the physics of the continuous measurement process, the strategy required to ideally uncollapse the wavefunction, as well as the statistical features associated with the measurement is discussed. We also summarize the recent experimental realization of two of these systems, the phase qubit and the polarization qubit.Comment: 19 pages, 4 figure

Methods for detection and characterization of signals in noisy data with the Hilbert-Huang Transform

The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency resolution but also renders it susceptible to degradation from noise. We show that complementing the HHT with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal to noise ratio.Comment: submitted to PRD, 10 pages, 9 figures in colo

Undoing a weak quantum measurement of a solid-state qubit

We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of the non-unitary nature of quantum measurement, though it is accompanied by a clear experimental indication of whether or not the undoing has been successful. The probability of success decreases with increasing strength of the measurement, reaching zero for a traditional projective measurement. Measurement undoing (``quantum un-demolition'') may be interpreted as a kind of a quantum eraser, in which the information obtained from the first measurement is erased by the second measurement, which is an essential part of the undoing procedure. The experiment can be realized using quantum dot (charge) or superconducting (phase) qubits.Comment: 5 page

Qubit feedback and control with kicked quantum nondemolition measurements: A quantum Bayesian analysis

The informational approach to continuous quantum measurement is derived from POVM formalism for a mesoscopic scattering detector measuring a charge qubit. Quantum Bayesian equations for the qubit density matrix are derived, and cast into the form of a stochastic conformal map. Measurement statistics are derived for kicked quantum nondemolition measurements, combined with conditional unitary operations. These results are applied to derive a feedback protocol to produce an arbitrary pure state after a weak measurement, as well as to investigate how an initially mixed state becomes purified with and without feedback.Comment: 13 pages, 3 figure

Ninja data analysis with a detection pipeline based on the Hilbert-Huang Transform

The Ninja data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert Huang Transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above SNR 5 in coincidence, with 43 missed events characterized by signal to noise ratio SNR less than 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a characterization of the event.Comment: Accepted for publication in CQG, special issue NRDA proceedings 200

Lithium in strong magnetic fields

The electronic structure of the lithium atom in a strong magnetic field 0 <= gamma <= 10 is investigated. Our computational approach is a full configuration interaction method based on a set of anisotropic Gaussian orbitals that is nonlinearly optimized for each field strength. Accurate results for the total energies and one-electron ionization energies for the ground and several excited states for each of the symmetries ^20^+, ^2(-1)^+, ^4(-1)^+, ^4(-1)^-, ^2(-2)^+, ^4(-2)^+, $^4(-3)^{+}$ are presented. The behaviour of these energies as a function of the field strength is discussed and classified. Transition wave lengths for linear and circular polarized transitions are presented as well.Comment: 12 pages, 13 figures, accepted for publication in Phys. Rev.

Evidence of hybridization between Galatella villosa and G. linosyris, and a taxonomic reappraisal of the hybrid G. xsubvillosa

At the westernmost distribution of the steppe herbaceous plant, Galatella villosa, in Hungary, Serbia and Ukraine, we recently observed intermediate specimens between this species and its close relative, G. linosyris. We were able to demonstrate the hybrid origin of these individuals by sequencing the biparentally inherited nuclear ribosomal internal transcribed spacer (nrITS) region and checking additive polymorphism in the hybrids. In addition, examination of the maternally inherited plastid regions (trnH-psbA and trnL-trnF intergenic spacers) revealed that G. villosa is likely to be the maternal parent in the Hungarian and Ukrainian populations and G. linosyris in the Serbian population. The intermediate forms produced only sterile seeds. The alleged hybrid between the above two species has already been described as G. xsubvillosa based on a very brief diagnosis. Still, the analysis of the morphological characters using linear discriminant analyses clearly separated the holotype of G. xsubvillosa from individuals of G. linosyris x G. villosa. The latter appeared to be morphologically intermediate between populations of G. villosa and G. linosyris. Contrary to the originally stated hybrid origin of the type plants of G. xsubvillosa, morphological evidence indicates the involvement of G. divaricata not G. linosyris. The hybrid G. linosyris x G. villosa is thus described here, as a new nothospecies G. xfeketegaborii. This study highlights the power of easily available molecular phylogenetic tools for demonstrating the hybrid origin of plants and illustrates how additive polymorphism can be distinguished from other types of intraindividual polymorphism in nuclear DNA sequences.Peer reviewe

Sparkling extreme-ultraviolet bright dots observed with Hi-C

Observing the Sun at high time and spatial scales is a step toward understanding the finest and fundamental scales of heating events in the solar corona. The high-resolution coronal (Hi-C) instrument has provided the highest spatial and temporal resolution images of the solar corona in the EUV wavelength range to date. Hi-C observed an active region on 2012 July 11 that exhibits several interesting features in the EUV line at 193 Å. One of them is the existence of short, small brightenings "sparkling" at the edge of the active region; we call these EUV bright dots (EBDs). Individual EBDs have a characteristic duration of 25 s with a characteristic length of 680 km. These brightenings are not fully resolved by the SDO/AIA instrument at the same wavelength; however, they can be identified with respect to the Hi-C location of the EBDs. In addition, EBDs are seen in other chromospheric/coronal channels of SDO/AIA, which suggests a temperature between 0.5 and 1.5 MK. Based on their frequency in the Hi-C time series, we define four different categories of EBDs: single peak, double peak, long duration, and bursty. Based on a potential field extrapolation from an SDO/HMI magnetogram, the EBDs appear at the footpoints of large-scale, trans-equatorial coronal loops. The Hi-C observations provide the first evidence of small-scale EUV heating events at the base of these coronal loops, which have a free magnetic energy of the order of 1026 erg. © 2014. The American Astronomical Society. All rights reserved

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Horizon Problem Remediation via Deformed Phase Space

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans-Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.Comment: 13 pages, 2 figures, to appear in GER