Gaussian systems for quantum enhanced multiple phase estimation

For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs and passive elements, by calculating the covariance matrix. The quantum Cram\'{e}r-Rao bound provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We prove that this bound can be saturated. In spite of the Gaussian nature of the problem, the calculation of non-Gaussian integrals is required, which we accomplish analytically. We find our simultaneous strategy to yield no more than a factor-of-2 improvement in total precision, possibly because of a fundamental performance limitation of Gaussian states. Our work shows that no modal entanglement is necessary for simultaneous quantum-enhanced estimation of multiple phases

Birth outcomes for African and Caribbean babies in England and Wales: retrospective analysis of routinely collected data

Objectives: To compare mean birth weights, gestational ages and odds of preterm birth and low birth weight of live singleton babies of black African or Caribbean ethnicity born in 2005 or 2006 by mother's country of birth. Design: Secondary analysis of data from linked birth registration and NHS Numbers for Babies data set. Setting: Births to women in England and Wales in 2005 and 2006. Participants: Babies of African and Caribbean ethnicity born in England and Wales in 2005–2006, whose mothers were born in African and Caribbean countries or the UK. Birth outcomes for 51 599 singleton births were analysed. Main outcome measures: Gestational age and birth weight. Results: Mothers born in Eastern or Northern Africa had babies at higher mean gestational ages (39.38 and 39.41 weeks, respectively) and lower odds of preterm birth (OR=0.80 and 0.65, respectively) compared with 39.00 weeks for babies with mothers born in the UK. Babies of African ethnicity whose mothers were born in Middle or Western Africa had mean birth weights of 3327 and 3311 g, respectively. These were significantly higher than the mean birth weight of 3257 g for babies of the UK-born mothers. Their odds of low birth weight (OR=0.75 and 0.72, respectively) were significantly lower. Babies of Caribbean ethnicity whose mothers were born in the Caribbean had higher mean birth weight and lower odds of low birth weight than those whose mothers were born in the UK. Conclusions: The study shows that in babies of African and Caribbean ethnicity, rates of low birth weight and preterm birth varied by mothers' countries of birth. Ethnicity and country of birth are important factors associated with perinatal health, but assessing them singly can mask important heterogeneity in birth outcomes within categories particularly in relation to African ethnicity. These differences should be explored further

Electrically driven magnetization of diluted magnetic semiconductors actuated by Overhauser effect

It is well-known that the Curie temperature, and hence the magnetization, in diluted magnetic semiconductor (DMS) like Ga$_{1-x}$Mn$_x$As can be controlled by changing the equilibrium density of holes in the material. Here, we propose that even with a constant hole density, large changes in the magnetization can be obtained with a relatively small imbalance in the quasi-Fermi levels for up-spin and down-spin electrons. We show, by coupling mean field theory of diluted magnetic semiconductor ferromagnetism with master equations governing the Mn spin-dynamics, that a mere splitting of the up-spin and down-spin quasi-Fermi levels by 0.1 meV will produce the effect of an external magnetic field as large as 1 T as long as the alternative relaxation paths for Mn spins (i.e. spin-lattice relaxation) can be neglected. The physics is similar to the classic Overhauser effect, also called the dynamic nuclear polarization, with the Mn impurities playing the role of the nucleus. We propose that a lateral spin-valve structure in anti-parallel configuration with a DMS as the channel can be used to demonstrate this effect as quasi-Fermi level splitting of such magnitude, inside the channel of similar systems, have already been experimentally demonstrated to produce polarization of paramagnetic impurity spins.Comment: Title, abstract and the body of the paper was modified although the basic conclusions remain unchanged. The modified version contains 7 pages, 4 figures

Linking maternity data for England 2007: methods and data quality

Maternity Hospital Episode Statistics (HES) data for 2007 were linked to birth registration and NHS Numbers for Babies (NN4B) data to bring together some key demographic and clinical data items not otherwise available at a national level. This extended the time period 2005-06, for which data had previously been linked and reported

Partial Isometries of a Sub-Riemannian Manifold

In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$. Then the pair $(H,g_H)$ defines a sub-Riemannian structure on $M$. We call a $C^1$-map $f:(M,H,g_H)\to (N,h)$ into a Riemannian manifold $(N,h)$ a {\em partial isometry} if the derivative map $df$ restricted to $H$ is isometric; in other words, $f^*h|_H=g_H$. The main result states that if $\dim N>k$ then a smooth $H$-immersion $f_0:M\to N$ satisfying $f^*h|_H<g_H$ can be homotoped to a partial isometry $f:(M,g_H)\to (N,h)$ which is $C^0$-close to $f_0$. In particular we prove that every sub-Riemannian manifold $(M,H,g_H)$ admits a partial isometry in $\R^n$ provided $n\geq m+k$.Comment: 13 pages. This is a revised version of an earlier submission (minor revision

Rapidly rotating strange stars for a new equation of state of strange quark matter

For a new equation of state of strange quark matter, we construct equilibrium sequences of rapidly rotating strange stars in general relativity. The sequences are the normal and supramassive evolutionary sequences of constant rest mass. We also calculate equilibrium sequences for a constant value of $\Omega$ corresponding to the most rapidly rotating pulsar PSR 1937 + 21. In addition to this, we calculate the radius of the marginally stable orbit and its dependence on $\Omega$, relevant for modeling of kilo-Hertz quasi-periodic oscillations in X-ray binaries.Comment: Two figures, uses psbox.tex and emulateapj5.st

Bounding the quantum limits of precision for phase estimation with loss and thermal noise

We consider the problem of estimating an unknown but constant carrier phase modulation $\theta$ using a general -- possibly entangled -- $n$-mode optical probe through $n$ independent and identical uses of a lossy bosonic channel with additive thermal noise. We find an upper bound to the quantum Fisher information (QFI) of estimating $\theta$ as a function of $n$, the mean and variance of the total number of photons $N_{\rm S}$ in the $n$-mode probe, the transmissivity $\eta$ and mean thermal photon number per mode ${\bar n}_{\rm B}$ of the bosonic channel. Since the inverse of QFI provides a lower bound to the mean-squared error (MSE) of an unbiased estimator $\tilde{\theta}$ of $\theta$, our upper bound to the QFI provides a lower bound to the MSE. It already has found use in proving fundamental limits of covert sensing, and could find other applications requiring bounding the fundamental limits of sensing an unknown parameter embedded in a correlated field.Comment: No major changes to previous version. Change in the title and abstract, change in the presentation and structure, an example of the bound is now included, and some references were added. Comments are welcom

On the Observability of "Invisible" / "Nearly Invisible" Charginos

It is shown that if the charginos decay into very soft leptons or hadrons + $\not{E}$ due to degeneracy/ near- degeneracy with the LSP or the sneutrino, the observability of the recently proposed signal via the single photon (+ soft particles) + $\not{E}$ channel crucially depends on the magnitude of the \SNU mass due to destructive interferences in the matrix element squared. If the \SNU's and, consequently, left-sleptons are relatively light, the size of the signal, previously computed in the limit \MSNU \to \infty only, is drastically reduced. We present the formula for the signal cross section in a model independent way and discuss the observability of the signal at LEP 192 and NLC energies.Comment: 27 pages, Late

Fundamental limits of quantum-secure covert optical sensing

We present a square root law for active sensing of phase $\theta$ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an $n$-mode covert optical probe, the mean squared error (MSE) of the resulting estimator $\hat{\theta}_n$ scales as $\langle (\theta-\hat{\theta}_n)^2\rangle=\mathcal{O}(1/\sqrt{n})$; improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, even when the adversary captures every photon that does not return to the sensor and performs arbitrarily complex measurement as permitted by the laws of quantum mechanics.Comment: 13 pages, 1 figure, submitted to ISIT 201