Quantum State Smoothing for Linear Gaussian Systems

Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified for Linear Gaussian quantum systems, which have wide physical applicability. We derive a closed-form solution for the quantum smoothed state, which is more pure than the standard filtered state, whilst still being described by a physical quantum state, unlike other proposed quantum smoothing techniques. We apply the theory to an on-threshold optical parametric oscillator, exploring optimal conditions for purity recovery by smoothing. The role of quantum efficiency is elucidated, in both low and high efficiency limits.Comment: 6 pages, 3 figures, 5 pages Supplemental Materia

Adaptive Phase Measurements in Linear Optical Quantum Computation

Photon counting induces an effective nonlinear optical phase shift on certain states derived by linear optics from single photons. Although this no nlinearity is nondeterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode -- so-called "single-rail" logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to "dual-rail" logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state $\alpha \ket{0} + \beta\ket{1}$ can be prepared deterministically

Assessment of sexual difficulties associated with multi-modal treatment for cervical or endometrial cancer: A systematic review of measurement instruments

Background: Practitioners and researchers require an outcome measure that accurately identifies the range of common treatment-induced changes in sexual function and well-being experienced by women after cervical or endometrial cancer. This systematic review critically appraised the measurement properties and clinical utility of instruments validated for the measurement of female sexual dysfunction (FSD) in this clinical population. Methods: A bibliographic database search for questionnaire development or validation papers was completed and methodological quality and measurement properties of selected studies rated using the Consensus-based Standards for the selection of health Measurement Instrument (COSMIN) checklist. Results: 738 articles were screened, 13 articles retrieved for full text assessment and 7 studies excluded, resulting in evaluation of 6 papers; 2 QoL and 4 female sexual morbidity measures. Five of the six instruments omitted one or more dimension of female sexual function and only one instrument explicitly measured distress associated with sexual changes as per DSM V (APA 2013) diagnostic criteria. None of the papers reported measurement error, responsiveness data was available for only two instruments, three papers failed to report on criterion validity, and test-retest reliability reporting was inconsistent. Heterosexual penile-vaginal intercourse remains the dominant sexual activity focus for sexual morbidity PROMS terminology and instruments lack explicit reference to solo or non-coital sexual expression or validation in a non-heterosexual sample. Four out of six instruments included mediating treatment or illness items such as vaginal changes, menopause or altered body image. Conclusions: Findings suggest that the Female Sexual Function Index (FSFI) remains the most robust sexual morbidity outcome measure, for research or clinical use, in sexually active women treated for cervical or endometrial cancer

Black hole thermodynamics from simulations of lattice Yang-Mills theory

We report on lattice simulations of 16 supercharge SU(N) Yang-Mills quantum mechanics in the 't Hooft limit. Maldacena duality conjectures that in this limit the theory is dual to IIA string theory, and in particular that the behavior of the thermal theory at low temperature is equivalent to that of certain black holes in IIA supergravity. Our simulations probe the low temperature regime for N <= 5 and the intermediate and high temperature regimes for N <= 12. We observe 't Hooft scaling and at low temperatures our results are consistent with the dual black hole prediction. The intermediate temperature range is dual to the Horowitz-Polchinski correspondence region, and our results are consistent with smooth behavior there. We include the Pfaffian phase arising from the fermions in our calculations where appropriate.Comment: 4 pages, 4 figure

Adaptive estimation of a time-varying phase with coherent states: smoothing can give an unbounded improvement over filtering

The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy - such as the $1/(4\bar{n})$ standard quantum limit with coherent states - do not apply. Here, restricting to coherent states, we are able to analytically obtain the achievable accuracy - the equivalent of the standard quantum limit - for a wide class of phase variation. In particular, we consider the case where the phase has Gaussian statistics and a power-law spectrum equal to $\kappa^{p-1}/|\omega|^p$ for large $\omega$, for some $p>1$. For coherent states with mean photon flux ${\cal N}$, we give the Quantum Cram\'er-Rao Bound on the mean-square phase error as $[p \sin (\pi/p)]^{-1}(4{\cal N}/\kappa)^{-(p-1)/p}$. Next, we consider whether the bound can be achieved by an adaptive homodyne measurement, in the limit ${\cal N}/\kappa \gg 1$ which allows the photocurrent to be linearized. Applying the optimal filtering for the resultant linear Gaussian system, we find the same scaling with ${\cal N}$, but with a prefactor larger by a factor of $p$. By contrast, if we employ optimal smoothing we can exactly obtain the Quantum Cram{\'e}r-Rao Bound. That is, contrary to previously considered ($p=2$) cases of phase estimation, here the improvement offered by smoothing over filtering is not limited to a factor of 2 but rather can be unbounded by a factor of $p$. We also study numerically the performance of these estimators for an adaptive measurement in the limit where ${\cal N}/\kappa$ is not large, and find a more complicated picture.Comment: 12 pages, 3 figure