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We present the results of a dust-reverberation survey of quasars at redshifts z<0.6. We found a delayed response of the K-band flux variation after the optical flux variation in 25 out of 31 targets, and obtained the lag time between them for 22 targets. Combined with the results for nearby Seyfert galaxies, we provide the largest homogeneous collection of K-band dust-reverberation data for 36 type 1 active galactic nuclei (AGNs). This doubles the sample and includes the most distant AGN and the largest lag so far measured. We estimated the optical luminosity of the AGN component of each target using three different methods: spectral decomposition, the flux-variation-gradient method, and image decomposition. We found a strong correlation between the reverberation radius for the innermost dust torus and the optical luminosity over a range of approximately four orders of magnitude in luminosity, as is already known for Seyfert galaxies. We estimated the luminosity distances of the AGNs based on their dust-reverberation lags, and found that the data in the redshift-distance diagram are consistent with the current standard estimates of the cosmological parameters. We also present the radius-luminosity relations for isotropic luminosity indicators such as the hard X-ray (14--195 keV), [OIV] 25.89 um, and mid-infrared (12 um) continuum luminosities, which are applicable to obscured AGNs., Comment: Accepted for publication in ApJ; Proof correction was applied

In Yoshii et al. (2014), we described a new method for measuring extragalactic distances based on dust reverberation in active galactic nuclei (AGNs), and we validated our new method with Cepheid variable stars. In this paper, we validate our new method with Type Ia supernovae (SNe Ia) which occurred in two of the AGN host galaxies during our AGN monitoring program: SN 2004bd in NGC 3786 and SN 2008ec in NGC 7469. Their multicolor light curves were observed and analyzed using two widely accepted methods for measuring SN distances, and the distance moduli derived are $\mu=33.47\pm 0.15$ for SN 2004bd and $33.83\pm 0.07$ for SN 2008ec. These results are used to obtain independently the distance measurement calibration factor, $g$. The $g$ value obtained from the SN Ia discussed in this paper is $g_{\rm SN} = 10.61\pm 0.50$ which matches, within the range of 1$\sigma$ uncertainty, $g_{\rm DUST} = 10.60$, previously calculated ab initio in Yoshii et al. (2014). Having validated our new method for measuring extragalactic distances, we use our new method to calibrate reverberation distances derived from variations of H$\beta$ emission in the AGN broad line region (BLR), extending the Hubble diagram to $z\approx 0.3$ where distinguishing between cosmologies is becoming possible., Comment: Astrophysical Journal Letters accepted

One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known symmetrized form of the master equation, which is formally equivalent to the wave equation in quantum mechanics apart from the fact that wave functions are always real. The origin of the unusual behaviors of the weak value such as the negative probability and the abnormal enhancement of some expectations becomes clearer in the present case, where the two-time conditional probability has no ambiguity of imaginary/complex values., Comment: Revised version from Arxiv:1109.4302. To appear in the proceedings of the Symposium on 'Interface between Quantum Information and Statistical Physics', to be published by World Scientific

The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the weak value in the quantum mechanics. A negative probability and abnormal expectations of some quantities remarkablely larger than their inherent norms are found in an example of a stochastic Ising spin system., Comment: Revised as Arxiv:1201.1329

When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subsystem and decoherence free subspace play essential r\^oles in our implementation. The recursive relations also show that the number of gates required to encode $m$ logical qubits increases linearly in $m$., Comment: 9 pages, 3 figures

We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $\sigma_x^{\otimes n}$, $\sigma_y^{\otimes n}$ and $\sigma_z^{\otimes n}$, where $n>2$ is the number of qubits encoding the codeword. It is proved that (i) $n$ qubits codeword encodes $(n-1)$ data qubits when $n$ is odd and (ii) $n$ qubits codeword implements a noiseless subsystem encoding $(n-2)$ data qubits when $n$ is even. Quantum circuits implementing these schemes are constructed., Comment: 11 pages, 2 figures

It is known that one can do quantum error correction without syndrome measurement, which is often done in operator quantum error correction (OQEC). However, the physical realization could be challenging, especially when the recovery process involves high-rank projection operators and a superoperator. We use operator theory to improve OQEC so that the implementation can always be done by unitary gates followed by a partial trace operation. Examples are given to show that our error correction scheme outperforms the existing ones in various scenarios., Comment: 10 pages

We propose a quantum error correction without error detection. A quantum state $\rho_0$ combined with an ancilla state $\sigma$ is encoded unitarily and an error operator is applied on the encoded state. The recovery operation then produces a tensor product state $\rho_0 \otimes \sigma'$. The decoding operation is combined with the recovery operation and the state $\rho_0$ is directly reproduced without referring to the code word. A higher rank projection operator required for a conventional operator quantum error correction is not necessary to implement. Encoding and the recovery operations are implemented with unitary operators only, which makes quantum error correction much easier than any other proposals., Comment: 8 pages, 3 figures

We examine whether the spectral energy distribution of optical continuum emission of active galactic nuclei (AGNs) changes during flux variation, based on accurate and frequent monitoring observations of 11 nearby Seyfert galaxies and QSOs carried out in the B, V, and I bands for seven years by the MAGNUM telescope. The multi-epoch flux data in any two different bands obtained on the same night show a very tight linear flux to flux relationship for all target AGNs. The flux of the host galaxy within the photometric aperture is carefully estimated by surface brightness fitting to available high-resolution HST images and MAGNUM images. The flux of narrow emission lines in the photometric bands is also estimated from available spectroscopic data. We find that the non-variable component of the host galaxy plus narrow emission lines for all target AGNs is located on the fainter extension of the linear regression line of multi-epoch flux data in the flux to flux diagram. This result strongly indicates that the spectral shape of AGN continuum emission in the optical region does not systematically change during flux variation. The trend of spectral hardening that optical continuum emission becomes bluer as it becomes brighter, which has been reported by many studies, is therefore interpreted as the domination of the variable component of the nearly constant spectral shape of an AGN as it brightens over the non-variable component of the host galaxy plus narrow lines, which is usually redder than AGN continuum emission., Comment: 47 pages, 29 figures, AASTeX, Accepted for publication in ApJ

The long-term optical and near infrared monitoring observations for a type 1 act ive galactic nucleus NGC 4151 were carried out for six years from 2001 to 2006 b y using the MAGNUM telescope, and delayed response of flux variations in the $K(2.2\mu m)$ band to those in the $V(0.55\mu m)$ band was clearly detected. Based on cross correlation analysis, we precisely measured a lag time $\Delta t$ for eight separate periods, and we found that $\Delta t$ is not constant changing be tween 30 and 70 days during the monitoring period. Since $\Delta t$ is the ligh t travel time from the central energy source out to the surrounding dust torus, this is the first convincing evidence that the inner radius of dust torus did ch ange in an individual AGN. In order to relate such a change of $\Delta t$ with a change of AGN luminosity $L$, we presented a method of taking an average of th e observed $V$-band fluxes that corresponds to the measured value of $\Delta t$, and we found that the time-changing track of NGC 4151 in the $\Delta t$ versus $L$ diagram during the monitoring period deviates from the relation of $\Delta t \propto L^{0.5}$ expected from dust reverberation. This result, combined with t he elapsed time from period to period for which $\Delta t$ was measured, indicat es that the timescale of dust formation is about one year, which should be taken into account as a new constraint in future studies of dust evolution in AGNs., Comment: 5 pages, 3 figures, To appear in the ApJ Letter

Physical and chemical stochastic processes described by the master equation are investigated. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master equation, the exact expression of the entropy production was recently derived by Gaspard using the Kolmogorov-Sinai entropy ({\em J.Stat.Phys.}, \textbf{117} (2004), 599; [Errata; \textbf{126} (2006), 1109 ]). Although Gaspard's expression is derived from a stochastic consideration, it should be noted that Gaspard's expression conincides with the thermodynamical expression. For the corresponding Fokker-Planck equation, by using the detailed imbalance relation which appears in the derivation process of the fluctuation theorem through the Onsger-Machlup theory, the entropy production is expressed in terms of the {\em irreversible circulation of fluctuation}, which was proposed by Tomita and Tomita ({\em Prog.Theor.Phys.}, \textbf{51} (1974), 1731). However, this expression for the corresponding Fokker-Planck equation differs from that of the entropy production for the master equation. This discrepancy is due to the difference between the master equation and the corresponding Fokker-Planck equation, namely the former treats discrete events, but the latter equation is an approximation of the former one. In fact, in the latter equation, the original discrete events are smoothed out. To overcome this difficulty, we propose the {\em path weight principle}. By using this principle, the modified expression of the entropy production for the corresponding Fokker-Planck equation coincides with that of the master equation (i.e., the thermodynamical expression) for a simple chemical reaction system and a diffusion system., Comment: 17pages, no figures, to appear in Progreess of Theoretical Physics, Vol. 119, No.4

We propose a new method of analysing a variable component for type 1 active galactic nuclei (AGNs) in the near-infrared wavelength region. This analysis uses a multiple regression technique and divides the variable component into two components originating in the accretion disk at the center of AGNs and from the dust torus that far surrounds the disk. Applying this analysis to the long-term $VHK$ monitoring data of MCG+08-11-011 that were obtained by the MAGNUM project, we found that the $(H-K)$-color temperature of the dust component is $T = 1635$K $\pm20$K, which agrees with the sublimation temperature of dust grains, and that the time delay of $K$ to $H$ variations is $\Delta t\approx 6$ days, which indicates the existence of a radial temperature gradient in the dust torus. As for the disk component, we found that the power-law spectrum of $f_\nu \propto \nu^\alpha$ in the $V$ to near-infrared $HK$ bands varies with a fixed index of $\alpha\approx -0.1$ -- +0.4, which is broadly consistent with the irradiated standard disk model. The outer part of the disk therefore extends out to a radial distance where the temperature decreases to radiate the light in the near-infrared., Comment: 10pages + 5figures, accepted by ApJL

Late-time BVRIJHK photometry of the peculiar Type Ic SN 2002ap, taken between 2002 June 12 and 2003 August 29 with the MAGNUM telescope, is presented. The light curve decline rate is derived in each band and the color evolution is studied through comparison with nebular spectra and with SN 1998bw. Using the photometry, the OIR bolometric light curve is built, extending from before light maximum to day 580 after explosion. The light curve has a late-time shape strikingly similar to that of the hypernova SN 1998bw. The decline rate changes from 0.018 mag/day between day 130 and 230 to 0.014 mag/day between day 270 and 580. To reproduce the late-time light curve, a dense core must be added to the 1-D hypernova model that best fits the early-time observations, bringing the ejecta mass from 2.5 Msun to 3 Msun without much change in the kinetic energy, which is 4 times 10^51 ergs. This is similar to the case of other hypernovae and suggests asymmetry. A large H-band bump developed in the spectral energy distribution after about day 300, probably caused by strong [Si I] 1.646 micron and 1.608 micron emissions. The near-infrared flux contribution increased simultaneously from <30% to >50% at day 580. The near-infrared light curves were compared with those of other Type Ib/c supernovae, among which SN 1983I seems similar to SN 2002ap both in the near-infrared and in the optical., Comment: 24pages, 9 figures, ApJ in press (10 June 2006, v644 1 issue). Acknowledgements updated

Observations of 226 AGNs in the near-infrared $J$, $H$, and $K'$ bands are presented along with the analysis of the observations for variability. Our sample consists mainly of Seyfert 1 AGNs and QSOs. About a quarter of the objects in each category are radio loud. The AGNs in the entire sample have the redshifts spanning the range from $z=0$ to 1, and the absolute magnitudes from $M_B=-29$ to -18. All the objects were observed twice and their variability was measured by differential photometry. A reduction method of differential photometry, optimized to the analysis of extended images, has been developed. The systematic error in variability arising from AGNs of highly extended images is estimated to be less than 0.01 mag in each of the $J$, $H$, and $K'$ bands. The systematic error arising from the flat fielding is negligible for most AGNs, although it is more than 0.1 mag for some particular cases. The overall average flat fielding error is 0.03 mag for the image pairs. We find that these systematic errors are superseded by statistical errors, and the overall average total systematic and statistical errors amounts to 0.05 mag in the measured variability in each band. We find that 58% of all the AGNs in the entire sample show variability of more than $2\sigma$, and 44% of more than $3\sigma$. This result holds independent of the $J$, $H$, and $K'$ bands. The detection rate of variability is higher for a subsample of higher photometric accuracy, and there appears no limit to this tendency. In particular, when we consider a subsample with small photometric errors of $\sigma<0.03$ mag, the rate of $2\sigma$ detection is 80%, and 64% for $3\sigma$ detection. This suggests that most AGNs are variable in the near-infrared.

Variability of 226 AGNs in the near-infrared $J$, $H$, and $K'$ bands is analyzed and discussed. An ensemble average for measured variabilities was obtained for various samples of the AGNs divided by absolute $B$-magnitude $M_B$, redshift $z$, and radio strength. All the samples in the $J$, $H$, and $K'$ bands are found to give significant ensemble variability, but no significant wavelength dependence is found. The ensemble variability in the entire sample combining the $J$, $H$, and $K'$ samples is $\Delta m\approx 0.22$ mag, while $\Delta m\approx 0.18$ mag for the radio-quiet AGNs and $\Delta m\approx 0.26$ mag for radio-loud AGNs. The ensemble variability for the radio-quiet AGNs shows no significant $M_B$-dependence, while showing positive $M_B$-dependence for the radio-loud AGNs. In any samples the measured variability shows positive correlation among different passbands, with the correlation coefficients of $r_{JH}$, $r_{HK'}$, and $r_{JK'}$ ranging from 0.6 to 0.9. For radio-quiet AGNs, the coefficient $r_{HK'}$ in a redshift range of $0.10.3$ and radio-loud AGNs with $z<0.3$, we cannot confirm such strong correlation among different passbands. All the features of near-infrared variability for the radio-quiet AGNs are consistent with a simple dust reverberation model of the central regions of AGNs. However, the features for the radio-loud AGNs are not fully explained by such a model, and a non-thermal variable component is suggested as a viable candidate for causing their large and fast variability in the near-infrared region.