A practical scheme for error control using feedback

We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols (for example Ahn et. al, PRA, 65, 042301 (2001)), is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit-flips. We also consider implementation in a solid-state quantum computation architecture and estimate the maximal error rate which could be corrected with current technology.Comment: 12 pages, 3 figures. Minor typographic change

Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects

The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond--Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.Comment: 24 pages, 3 figures, previously known as "A User Manual for the Fisher Information Matrix"; final, corrected PRD versio

Signal Processing

Contains reports on three research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Notes on the integration of numerical relativity waveforms

A primary goal of numerical relativity is to provide estimates of the wave strain, $h$, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, $\psi_4$. Assuming Bondi gauge, transforming to the strain $h$ reduces to integration of $\psi_4$ twice in time. Integrations performed in either the time or frequency domain, however, lead to secular non-linear drifts in the resulting strain $h$. These non-linear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular non-linear drifts in the resulting strain.Comment: 23 pages, 10 figures, matches final published versio

Unambiguous comparison of the states of multiple quantum systems

We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states of all N systems are different. We investigate the possibility of unambiguously obtaining this kind of information. It is found that some unambiguous comparison tasks are possible only when certain linear independence conditions are satisfied. We also obtain measurement strategies for certain comparison tasks which are optimal under a broad range of circumstances, in particular when the states are completely unknown. Such strategies, which we call universal comparison strategies, are found to have intriguing connections with the problem of quantifying the distinguishability of a set of quantum states and also with unresolved conjectures in linear algebra. We finally investigate a potential generalisation of unambiguous state comparison, which we term unambiguous overlap filtering.Comment: 20 pages, no figure

Three-dimensional sound propagation models using the parabolic-equation approximation and the split-step Fourier method

Author Posting. © IMACS, 2012. This article is posted here by permission of World Scientific Publishing for personal use, not for redistribution. The definitive version was published in Journal of Computational Acoustics 21 (2013): 1250018, doi:10.1142/S0218396X1250018X.The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, θ, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domain, and has errors that increase with azimuthal angle from the x axis. The cylindrical model has consistent validity in each azimuthal direction, but a fixed cylindrical grid of radials cannot produce uniform resolution. Two different methods to achieve more uniform resolution in the cylindrical PE model are presented. One of the methods is to increase the grid points in azimuth, as a function of r, according to nonaliased sampling theory. The other is to make use of a fixed arc-length grid. In addition, a point-source starter is derived for the three-dimensional Cartesian PE model. Results from idealized seamount and slope calculations are shown to compare and verify the performance of the three methods.This work was sponsored by the Office of Naval Research under the grants N00014-10-1-0040 and N00014-11-1-0701

The spectrum of quantum black holes and quasinormal modes

The spectrum of multiple level transitions of the quantum black hole is considered, and the line widths calculated. Initial evidence is found for these higher order transitions in the spectrum of quasinormal modes for Schwarzschild and Kerr black holes, further bolstering the idea that there exists a correspondence principle between quantum transitions and classical ``ringing modes''. Several puzzles are noted, including a fine-tuning problem between the line width and the level degeneracy. A more general explanation is provided for why setting the Immirzi parameter of loop quantum gravity from the black hole spectrum necessarily gives the correct value for the black hole entropy.Comment: 5 pages, 5 figures, version to appear in Phys. Rev.

How uncertainty enables non-classical dynamics

The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance between different paths of an interferometer should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle, that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimises certainty in return for maximal non-classical dynamics.Comment: 4 pages + 4 page technical supplement, 2 figure

Monogamy of entanglement and other correlations

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the "monogamous nature of entanglement". In this paper we present a simple identity which captures the trade-off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade-offs of a monogamy nature for other entanglement measures and secret and total correlation measures.Comment: 7 pages, revtex

Signal velocity, causality, and quantum noise in superluminal light pulse propagation

We consider pulse propagation in a linear anomalously dispersive medium where the group velocity exceeds the speed of light in vacuum (c) or even becomes negative. A signal velocity is defined operationally based on the optical signal-to-noise ratio, and is computed for cases appropriate to the recent experiment where such a negative group velocity was observed. It is found that quantum fluctuations limit the signal velocity to values less than c.Comment: 4 Journal pages, 3 figure