Effect of frequency mismatched photons in quantum information processing

Many promising schemes for quantum information processing (QIP) rely on few-photon interference effects. In these proposals, the photons are treated as being indistinguishable particles. However, single photon sources are typically subject to variation from device to device. Thus the photons emitted from different sources will not be perfectly identical, and there will be some variation in their frequencies. Here, we analyse the effect of this frequency mismatch on QIP schemes. As examples, we consider the distributed QIP protocol proposed by Barrett and Kok, and Hong-Ou-Mandel interference which lies at the heart of many linear optical schemes for quantum computing. In the distributed QIP protocol, we find that the fidelity of entangled qubit states depends crucially on the time resolution of single photon detectors. In particular, there is no reduction in the fidelity when an ideal detector model is assumed, while reduced fidelities may be encountered when using realistic detectors with a finite response time. We obtain similar results in the case of Hong-Ou-Mandel interference -- with perfect detectors, a modified version of quantum interference is seen, and the visibility of the interference pattern is reduced as the detector time resolution is reduced. Our findings indicate that problems due to frequency mismatch can be overcome, provided sufficiently fast detectors are available.Comment: 14 pages, 8 figures. Comments welcome. v2: Minor changes. v3: Cleaned up 3 formatting error

A trend-preserving bias correction – The ISI-MIP approach

Statistical bias correction is commonly applied within climate impact modelling to correct climate model data for systematic deviations of the simulated historical data from observations. Methods are based on transfer functions generated to map the distribution of the simulated historical data to that of the observations. Those are subsequently applied to correct the future projections. Here, we present the bias correction method that was developed within ISI-MIP, the first Inter-Sectoral Impact Model Intercomparison Project. ISI-MIP is designed to synthesise impact projections in the agriculture, water, biome, health, and infrastructure sectors at different levels of global warming. Bias-corrected climate data that are used as input for the impact simulations could be only provided over land areas. To ensure consistency with the global (land + ocean) temperature information the bias correction method has to preserve the warming signal. Here we present the applied method that preserves the absolute changes in monthly temperature, and relative changes in monthly values of precipitation and the other variables needed for ISI-MIP. The proposed methodology represents a modification of the transfer function approach applied in the Water Model Intercomparison Project (Water-MIP). Correction of the monthly mean is followed by correction of the daily variability about the monthly mean. Besides the general idea and technical details of the ISI-MIP method, we show and discuss the potential and limitations of the applied bias correction. In particular, while the trend and the long-term mean are well represented, limitations with regards to the adjustment of the variability persist which may affect, e.g. small scale features or extremes

Stochastic simulations of conditional states of partially observed systems, quantum and classical

In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional state will be given by a state matrix $\rho_r(t)$ and if classical the conditional state will be given by a probability distribution $P_r(x,t)$ where $r$ is the result of the measurement. Thus to determine the evolution of this conditional state under continuous-in-time monitoring requires an expensive numerical calculation. In this paper we demonstrating a numerical technique based on linear measurement theory that allows us to determine the conditional state using only pure states. That is, our technique reduces the problem size by a factor of $N$, the number of basis states for the system. Furthermore we show that our method can be applied to joint classical and quantum systems as arises in modeling realistic measurement.Comment: 16 pages, 11 figure

Detecting the redshifted 21cm forest during reionization

The 21cm forest -- HI absorption features in the spectra of high-redshift radio sources -- can potentially provide a unique probe of the largely neutral intergalactic medium (IGM) during the epoch of reionization. We present simulations of the 21cm forest due to the large scale structure of the reionization-era IGM, including a prescription for x-ray heating and the percolation of photoionization bubbles. We show that, if detected with future instruments such as the Square Kilometer Array (SKA), the 21cm forest can provide a significant constraint on the thermal history of the IGM. Detection will be aided by consideration of the sudden increase in signal variance at the onset of 21cm absorption. If radio foregrounds and the intrinsic source spectra are well understood, the flux decrement over wide bandwidths can also improve detection prospects. Our analysis accounts for the possibility of narrow absorption lines from intervening dense regions, but, unlike previous studies, our results do not depend on their properties. Assuming x-ray heating corresponding to a local stellar population, we estimate that a statistically significant detection of 21cm absorption could be made by SKA in less than a year of observing against a Cygnus A-type source at $z \sim 9$, as opposed to nearly a decade for a significant detection of the detailed forest features. We discuss observational challenges due to uncertainties regarding the abundance of background sources and the strength of the 21cm absorption signal.Comment: Submitted to MNRAS. Revised version includes updated and extended calculations, some corrections and added reference

Observations of microglitches in HartRAO radio pulsars

A detailed observation of microglitch phenomenon in relatively slow radio pulsars is presented. Our analyses for these small amplitude jumps in pulse rotation frequency ($\nu$) and/or spin down rate ($\dot{\nu}$) combine the traditional manual detection method (which hinges on careful visual inspections of the residuals of pulse phase residuals) and a new, and perhaps more objective, automated search technique (which exploits the power of the computer, rather than the eyes, for resolving discrete events in pulsar spin parameters). The results of the analyses of a sample of 26 radio pulsars reveal that: (i) only 20 pulsars exhibit significant fluctuations in their arrival times to be considered suitable for meaningful microglitch analyses; (ii) a phenomenal 299 microglitch events were identified in $\nu$ and/or $\dot{\nu}$: 266 of these events were found to be simultaneously significant in $\nu$ and $\dot{\nu}$, while 19 and 14 were noticeable only in $\nu$ and $\dot{\nu}$, respectively; (iii) irrespective of sign, the microglitches have fractional sizes which cover about 3 orders of magnitude in $\nu$ and $\dot{\nu}$ ($10^{-11} < |\Delta{\nu}/\nu| < 2.0\times10^{-8}$ and $5.0\times10^{-5} < |\Delta{\dot{\nu}}/\dot{\nu}| < 2.0\times10^{-2}$) with median values as $0.78\times10^{-9}$ and $0.36\times10^{-3}$, respectively.Comment: 12 pages, 3 figures, 2 Tables. Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman and H. Mabuchi, Phys. Rev. A_65_ 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the ``realistic quantum trajectories'' of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.Comment: 7 pages, 2 figures. Shorter, significantly modified, updated versio

The Impact of HI in Galaxies on 21-cm Intensity Fluctuations During the Reionisation Epoch

We investigate the impact of neutral hydrogen (HI) in galaxies on the statistics of 21-cm fluctuations using analytic and semi-numerical modelling. Following the reionisation of hydrogen the HI content of the Universe is dominated by damped absorption systems (DLAs), with a cosmic density in HI that is observed to be constant at a level equal to ~2% of the cosmic baryon density from z~1 to z~5. We show that extrapolation of this constant fraction into the reionisation epoch results in a reduction of 10-20% in the amplitude of 21-cm fluctuations over a range of spatial scales. The assumption of a different percentage during the reionisation era results in a proportional change in the 21-cm fluctuation amplitude. We find that consideration of HI in galaxies/DLAs reduces the prominence of the HII region induced shoulder in the 21-cm power spectrum (PS), and hence modifies the scale dependence of 21-cm fluctuations. We also estimate the 21cm-galaxy cross PS, and show that the cross PS changes sign on scales corresponding to the HII regions. From consideration of the sensitivity for forthcoming low-frequency arrays we find that the effects of HI in galaxies/DLAs on the statistics of 21-cm fluctuations will be significant with respect to the precision of a PS or cross PS measurement. In addition, since overdense regions are reionised first we demonstrate that the cross-correlation between galaxies and 21-cm emission changes sign at the end of the reionisation era, providing an alternative avenue to pinpoint the end of reionisation. The sum of our analysis indicates that the HI content of the galaxies that reionise the universe will need to be considered in detailed modelling of the 21-cm intensity PS in order to correctly interpret measurements from forthcoming low-frequency arrays.Comment: 11 pages, 6 figures. Submitted to MNRA

Modification of the 21-cm power spectrum by X-rays during the epoch of reionisation

We incorporate a contribution to reionization from X-rays within analytic and semi-numerical simulations of the 21-cm signal arising from neutral hydrogen during the epoch of reionization. We explore the impact that X-ray ionizations have on the power spectrum (PS) of 21-cm fluctuations by varying both the average X-ray MFP and the fractional contribution of X-rays to reionization. In general, prior to the epoch when the intergalactic medium is dominated by ionized regions (H {\sevensize II} regions), X-ray-induced ionization enhances fluctuations on spatial scales smaller than the X-ray MFP, provided that X-ray heating does not strongly supress galaxy formation. Conversely, at later times when \H2 regions dominate, small-scale fluctuations in the 21-cm signal are suppressed by X-ray ionization. Our modelling also shows that the modification of the 21-cm signal due to the presence of X-rays is sensitive to the relative scales of the X-ray MFP, and the characteristic size of \H2 regions. We therefore find that X-rays imprint an epoch and scale-dependent signature on the 21-cm PS, whose prominence depends on fractional X-ray contribution. The degree of X-ray heating of the IGM also determines the extent to which these features can be discerned. We show that the MWA will have sufficient sensitivity to detect this modification of the PS, so long as the X-ray photon MFP falls within the range of scales over which the array is most sensitive ($\sim0.1$ Mpc$^{-1}$). In cases in which this MFP takes a much smaller value, an array with larger collecting area would be required.Comment: 15 pages, 6 figures, Accepted for publication in MNRAS X-ray heating contribution now adde

Adiabatic Elimination in Compound Quantum Systems with Feedback

Feedback in compound quantum systems is effected by using the output from one sub-system (``the system'') to control the evolution of a second sub-system (``the ancilla'') which is reversibly coupled to the system. In the limit where the ancilla responds to fluctuations on a much shorter time scale than does the system, we show that it can be adiabatically eliminated, yielding a master equation for the system alone. This is very significant as it decreases the necessary basis size for numerical simulation and allows the effect of the ancilla to be understood more easily. We consider two types of ancilla: a two-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g. an optical mode). For each, we consider two forms of feedback: coherent (for which a quantum mechanical description of the feedback loop is required) and incoherent (for which a classical description is sufficient). We test the master equations we obtain using numerical simulation of the full dynamics of the compound system. For the system (a parametric oscillator) and feedback (intensity-dependent detuning) we choose, good agreement is found in the limit of heavy damping of the ancilla. We discuss the relation of our work to previous work on feedback in compound quantum systems, and also to previous work on adiabatic elimination in general.Comment: 18 pages, 12 figures including two subplots as jpeg attachment