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287
From Physics to Number theory via Noncommutative Geometry, II  Chapter 2: Renormalization, The RiemannHilbert correspondence, and . . .
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Feedback Control of Quantum State Reduction
, 2004
"... Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for th ..."
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Cited by 37 (4 self)
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Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.
The photon counting histogram in fluorescence fluctuation spectroscopy with nonideal photodetectors
 Biophys. J
, 2003
"... ABSTRACT Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH ..."
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Cited by 30 (9 self)
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ABSTRACT Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH) analysis constitutes a novel tool for extracting quantities from fluorescence fluctuation data, i.e., the measured photon counts per molecule and the average number of molecules within the observation volume. The photon counting histogram of fluorescence fluctuation experiments, in which few molecules are present in the excitation volume, exhibits a superPoissonian behavior. The additional broadening of the PCH compared to a Poisson distribution is due to fluorescence intensity fluctuations. For diffusing particles these intensity fluctuations are caused by an inhomogeneous excitation profile and the fluctuations in the number of particles in the observation volume N #. The quantitative relationship between the detected photon counts and the fluorescence intensity reaching the detector is given by Mandel’s formula. Based on this equation and considering the fluorescence intensity distribution in the twophoton excitation volume, a theoretical expression for the PCH as a function of the number of molecules in the excitation volume is derived. For a single molecular species two parameters are sufficient to characterize the histogram completely, namely the average number of molecules within the observation volume and the detected photon counts per molecule per sampling time e. The PCH for multiple molecular species, on the other hand, is generated by successively convoluting the photon counting distribution of each species with the others. The influence of the excitation
Interferometric synthetic aperture microscopy: physicsbased image reconstruction from optical coherence tomography data
 In International Conference on Image Processing
, 2007
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Time reversal refocusing for point source in randomly layered media, Wave Motion 42
, 2005
"... Abstract. This paper demonstrates the interest of a timereversal method for the identification of source in a randomly layered medium. An active source located inside the medium emits a pulse that is recorded on a small timereversal mirror. The wave is sent back into the medium, either numerically ..."
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Cited by 15 (7 self)
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Abstract. This paper demonstrates the interest of a timereversal method for the identification of source in a randomly layered medium. An active source located inside the medium emits a pulse that is recorded on a small timereversal mirror. The wave is sent back into the medium, either numerically in a computer with the knowledge of the medium, or physically into the real medium. Our goal is to give a precise description of the refocusing of the pulse. We identify and analyze a regime where the pulse refocuses on a ring at the depth of the source and at a critical time. Our objective is to find the location of the source and we show that the timereveresal refocusing contains information which can be used to this effect and which cannot be obtained by a direct arrivaltime analysis. The time reversal technique gives a robust procedure to locate and characterize the source also in the case with ambient noise created by other sources located at the surface. Key words. Acoustic waves, random media, asymptotic theory, time reversal. AMS subject classifications. 76B15, 35Q99, 60F05. 1. Introduction. In
Research on hidden variable theories: a review of recent progresses
, 2007
"... Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various aspects concerning its very foundations still remain to be c ..."
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Cited by 12 (0 self)
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Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various aspects concerning its very foundations still remain to be clarified. Among them, the transition from a microscopic probabilistic world into a macroscopic deterministic one and quantum nonlocality. A possible way out from these problems would be if QM represents a statistical approximation of an unknown deterministic theory. This review is addressed to present the most recent progresses on the studies related to Hidden Variable Theories (HVT), both from an experimental and a theoretical point of view, giving a larger emphasis to results with a direct experimental application. More in details, the first part of the review is a historical introduction to this problem. The EinsteinPodolskyRosen argument and the first discussions about
A Discrete Invitation to Quantum Filtering and Feedback Control
, 2009
"... The engineering and control of devices at the quantum mechanical level—such as those consisting of small numbers of atoms and photons—is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a nov ..."
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Cited by 12 (2 self)
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The engineering and control of devices at the quantum mechanical level—such as those consisting of small numbers of atoms and photons—is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory while remaining completely within the setting of finitedimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.
How to Build Unconditionally Secure Quantum Bit Commitment Protocols”, quantph 0305144
"... Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. It is widely believed that secure quantum bit commitm ..."
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Cited by 12 (4 self)
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Bit commitment involves the submission of evidence from one party to another so that the evidence can be used to confirm a later revealed bit value by the first party, while the second party cannot determine the bit value from the evidence alone. It is widely believed that secure quantum bit commitment is impossible due to quantum entanglement cheating, which is codified in a general impossibility theorem. An unconditionally secure bit commitment protocol utilizing quantum states is presented below, in which the second party can deliberately destroy the entanglement needed for the first party to cheat successfully.