Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough

To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $\rho$ is maximally different, or complementary, to the measured observable. This requires the ability to perform unitary operations on the state, conditioned on the results of prior measurements. We consider the case of measurement of a component of angular momentum for a qudit (a $D$-dimensional system, with $D=2J+1$). For weak or continuous-in-time (i.e. repeated weak) measurements, we show that the complementarity condition ensures an average improvement, in the rate of purification, of only 2. However, we show that by choosing the optimal control protocol of this type, one can attain the best possible scaling, $O(D^{2})$, for the average improvement. For this protocol the acquisition of information is nearly deterministic. Finally we contrast these results with those for complementarity-based protocols in a register of qbits.Comment: 21 pages, 21 figures. V2 published versio

Quantum feedback for rapid state preparation in the presence of control imperfections

Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an $x$ eigenstate from a mixed state in the minimum time, and is known as rapid state preparation. The imperfections we examine include time delays in the feedback loop, finite strength feedback, calibration errors, and inefficient detection. We analyse these imperfections using the Wiseman-Milburn feedback master equation and related formalism. We find that the protocol is most sensitive to time delays in the feedback loop. For systems with slow dynamics, however, our analysis suggests that inefficient detection would be the bigger problem. We also show how system imperfections, such as dephasing and damping, can be included in model via the feedback master equation.Comment: 15 pages, 6 figures and 2 tables. V2 the published version, fig. 1 corrected and some minor changes to the tex

The overmassive black hole in NGC 1277: new constraints from molecular gas kinematics

We report the detection of CO(1-0) emission from NGC 1277, a lenticular galaxy in the Perseus Cluster. NGC 1277 has previously been proposed to host an overmassive black hole (BH) compared to the galaxy bulge luminosity (mass), based on stellar-kinematic measurements. The CO(1-0) emission, observed with the IRAM Plateau de Bure Interferometer (PdBI) using both, a more compact (2.9-arcsec resolution) and a more extended (1-arcsec resolution) configuration, is likely to originate from the dust lane encompassing the galaxy nucleus at a distance of 0.9 arcsec (~320 pc). The double-horned CO(1-0) profile found at 2.9-arcsec resolution traces $1.5\times 10^8\ M_\odot$ of molecular gas, likely orbiting in the dust lane at $\sim 550\ \mathrm{km\ s^{-1}}$, which suggests a total enclosed mass of$\sim 2\times 10^{10}\ M_\odot$. At 1-arcsec resolution, the CO(1-0) emission appears spatially resolved along the dust lane in east-west direction, though at a low signal-to-noise ratio. In agreement with the previous stellar-kinematic measurements, the CO(1-0) kinematics is found to be consistent with an$\sim 1.7\times 10^{10}\ M_\odot$BH for a stellar mass-to-light ratio of$M/L_V=6.3$, while a less massive BH of$\sim 5\times 10^{9}\ M_\odot$is possible when assuming a larger$M/L_V=10$. While the molecular gas reservoir may be associated with a low level of star formation activity, the extended 2.6-mm continuum emission is likely to originate from a weak AGN, possibly characterized by an inverted radio-to-millimetre spectral energy distribution. Literature radio and X-ray data indicate that the BH in NGC 1277 is also overmassive with respect to the Fundamental Plane of BH activity.Comment: 15 pages, 13 figures; accepted for publication in MNRAS on 20 January 2016; updated version including minor changes and note added in proo

Conductivity and the current-current correlation measure

We review various formulations of conductivity for one-particle Hamiltonians and relate them to the current-current correlation measure. We prove that the current-current correlation measure for random Schr\"odinger operators has a density at coincident energies provided the energy lies in a localization regime. The density vanishes at such energies and an upper bound on the rate of vanishing is computed. We also relate the current-current correlation measure to the localization length

Quantum limits on phase-preserving linear amplifiers

The purpose of a phase-preserving linear amplifier is to make a small signal larger, regardless of its phase, so that it can be perceived by instruments incapable of resolving the original signal, while sacrificing as little as possible in signal-to-noise. Quantum mechanics limits how well this can be done: a high-gain linear amplifier must degrade the signal-to-noise; the noise added by the amplifier, when referred to the input, must be at least half a quantum at the operating frequency. This well-known quantum limit only constrains the second moments of the added noise. Here we derive the quantum constraints on the entire distribution of added noise: we show that any phase-preserving linear amplifier is equivalent to a parametric amplifier with a physical state for the ancillary mode; the noise added to the amplified field mode is distributed according to the Wigner function of the ancilla state.Comment: 37 pages, 6 figure

First Detection of Molecular Gas in the Shells of CenA

Shells are faint arc-like stellar structures, which have been observed around early type galaxies and are thought to be the result of an interaction. HI gas has recently been detected in shells, a surprising result in view of the theoretical predictions that most of the gas should decouple from stars and fall into the nucleus in such interactions. Here we report the first detection of molecular gas (CO) in shells, found 15kpc away from the center of NGC5128 (CenA), a giant elliptical galaxy that harbors an active nucleus (AGN). The ratio between CO and HI emission in the shells is the same as that found in the central regions, which is unexpected given the metallicity gradient usually observed in galaxies. We propose that the dynamics of the gas can be understood within the standard picture of shell formation if one takes into account that the interstellar medium is clumpy and hence not highly dissipative. The observed metal enrichment could be due to star formation induced by the AGN jet in the shells. Furthermore our observations provide evidence that molecular gas in mergers may be spread out far from the nuclear regions.Comment: Accepted for publication in Astronomy & Astrophysics Letters, (Vol. 356), 4 pages + 1 color figur

Quantifying stellar radial migration in an N-body simulation: blurring, churning, and the outer regions of galaxy discs

Radial stellar migration in galactic discs has received much attention in studies of galactic dynamics and chemical evolution, but remains a dynamical phenomenon that needs to be fully quantified. In this work, using a Tree-SPH simulation of an Sb-type disc galaxy, we quantify the effects of blurring (epicyclic excursions) and churning (change of guiding radius). We quantify migration (either blurring or churning) both in terms of flux (the number of migrators passing at a given radius), and by estimating the population of migrators at a given radius at the end of the simulation compared to non-migrators, but also by giving the distance over which the migration is effective at all radii. We confirm that the corotation of the bar is the main source of migrators by churning in a bar-dominated galaxy, its intensity being directly linked to the episode of a strong bar, in the first 1-3 Gyr of the simulation. We show that within the outer Lindblad resonance (OLR), migration is strongly dominated by churning, while blurring gains progressively more importance towards the outer disc and at later times. Most importantly, we show that the OLR limits the exchange of angular momentum, separating the disc in two distinct parts with minimal or null exchange, except in the transition zone, which is delimited by the position of the OLR at the epoch of the formation of the bar, and at the final epoch. We discuss the consequences of these findings for our understanding of the structure of the Milky Way disc. Because the Sun is situated slightly outside the OLR, we suggest that the solar vicinity may have experienced very limited churning from the inner disc.Comment: Accepted for publication in Astronomy and Astrophysics (acceptance date: 27/04/15), 24 pages, 24 figure

On Eigenvalue spacings for the 1-D Anderson model with singular site distribution

We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main additional new input are regular properties of the Furstenberg measures and the density of states obtained in some of the author's earlier work.Comment: 13 page