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As shown in Figure 41b the laboratory implementation of the closed-loop measurement consists in the following Light from an external-cavity grating-stabilized diode laser 4) operating at 852nm is coupled into a polarization-maintaining beroptic Mach Zehnder interferometer A Mach Zehnder interferometer is a device used to determine the phase shift caused by a small sample which is placed in the path of one of two collimated beams (thus having plane wave fronts) from a coherent light source The input beamsplitter (FBS1) provides two optical elds with a well-de ned relative phase: the upper arm of the interferometer acts as the target quantum system for state discrimination and the lower arm provides an auxiliary eld used to perform closed-loop displacements at the second beamsplitter (FBS2) Photon counting on the outcoupled eld is implemented using a gated silicon avalanche photodiode (APD) APDs are photodetectors that can be regarded as the semiconductor analog of photomultipliers By applying a high reverse bias voltage (typically 100 200 V in silicon), APDs show an internal current gain effect (around 100) due to impact ionization (avalanche effect) The feedback controller is constructed from a combination of programmable waveform generators and high-speed digital signal processing electronics (feedback bandwidth 30 MHz) A digital counter records the number of photon counter clicks generated in each measurement interval [0, ], during which time the feedback controller determines the feedback amplitude u n [0,t] in (444) via the accumulating count record n [0,t) t Coherent states for discrimination are realized as = 20 s optical pulses produced by a computer-controlled polarization-maintaining ber-optic intensity modulator (FIM1) in the upper arm of the interferometer The calibration parity between desired and observed values of in Figure 42a (squares) highlights the ability to prepare arbitrary optical coherent states with amplitudes 01 u | | u 1 Counting statistics for one such preparation with the mean photon number n = |N | = | |2 are shown in the inset The circles in the inset are a Poisson t to the counting data, for which 2 1 has been computed below 1ppm, showing the quantum noise-limitation of the state preparation The phase of the prepared coherent states ( ) and the phase of the feedback displacements (u t ) are implemented by the modulator (FPM) in the upper arm of the interferometer Without loss of generality, ( ) = 0 was always chosen to simplify the interpretation of the displacements.



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Americans are in worse shape than most believe It should come as no surprise that as the world s richest country the United States leads the way in terms of lifestyle diseases Chronic illnesses account for roughly 70 percent of health costs and deaths in the United States,3 well above the 60 percent global average4 The nation has witnessed a quadrupling in the rate of childhood obesity and a doubling in the asthma rate over the past 30 years5 But what may come as a surprise is that the United States spends more than any other country on health care a whopping $23 trillion in 2007, or $7,600 per person yet the country still ranked only 38 out of 195 in terms of life expectancy6





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NeOCR is a free software based on Tesseract ( Open Source OCR Engine) for the Windows operating system. It provides an easy and user-friendly user interface to recognize texts contained in images as well as PDF documents and convert to editable text formats (.txt, .doc, .docx).

4) From Encyclopedia of Laser Physics and Technology, http://wwwrp-photonicscom/: An external-cavity diode laser is a semiconductor laser based on a laser diode chip which typically has one end antire ection coated, and the laser resonator is completed with, eg, a collimating lens and an external mirror

Fig 42 (a) Quality of the preparation of the optical coherent states (circles) and the control of the displacements (squares) The inset shows a Poisson t of the photon counting statistics for W 1, illustrating the quantum limitation of the state preparation (b) Quality of the implementation of the controlled phase displacements ( u t ) The calibration in (b) illustrates the low control voltages (V ) required to drive the apparatus, which allows

for high-bandwidth application of the measurement feedback control Each data point in (a) and (b) re ects a statistical ensemble of 100 000 replicate measurements, with error bars given by the estimated sample standard deviation Source Cook et al [40] (reprinted by permission from Macmillan Publishers Limited: [Nature] (Cook, RL, Martin, PJ, and Geremia, JM 446, p 774, 2007))

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Residual technical imperfections in the experiment result primarily from detector dark counts ( d = 00078), interferometer phase noise ( W 8 mrad), and nite n extinction of the modulators

The measured probability of error versus mean photon number is shown in Figure 43a The squares correspond to the case in which the feedback is disabled The circles correspond to the closed-loop measurement

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4731 Disabled Feedback The measurement reduces to direct photon counting The observed probability of error for discriminating between |0 and | faithfully reproduces shot noise (line with squares) as a function of n To get a precise view of the experimental challenge, data points were calculated using 100 000 optical pulses sampled randomly from {|0 , | } with equal probability The label |0 has been used to signify the darkest eld n 0 W 0008 The residual eld appears to have a negligible effect, with a discrepancy of 2 1 = 113 ~ 10 5 between the photon counting data in Fign ure 43a and the shot-noise error probability de ned as P SN = e /2

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Fig 43 (a) The measured probability of error versus mean photon number for both direct photon counting (squares) and the Cook Martin Geremia closed-loop measurement interpreted using a Bayesian estimator that assumes application of the optimal closedloop control policy (circles) and that accounts for experimental imperfections (triangles) All data points were obtained from ensembles of 100 000 measurement trajectories, with error bars that re ect the sample standard deviation The four traces in (b) (1 4) depict a single-shot closed-loop

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