Quantum process tomography of a controlled-NOT gate

We demonstrate complete characterization of a two-qubit entangling process-a linear optics controlled-NOT gate operating with coincident detection-by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.

Quantum phase-space analysis of the pendular cavity

We perform a quantum-mechanical analysis of the pendular cavity, using the positive-P representation, showing that the quantum state of the moving mirror, a macroscopic object, has noticeable effects on the dynamics. This system has previously been proposed as a candidate for the quantum-limited measurement of small displacements of the mirror due to radiation pressure, for the production of states with entanglement between the mirror and the field, and even for superposition states of the mirror. However, when we treat the oscillating mirror quantum mechanically, we find that it always oscillates, has no stationary steady state, and exhibits uncertainties in position and momentum which are typically larger than the mean values. This means that previous linearized fluctuation analyses which have been used to predict these highly quantum states are of limited use. We find that the achievable accuracy in measurement is fat, worse than the standard quantum limit due to thermal noise, which, for typical experimental parameters, is overwhelming even at 2 mK

Anharmonic effects on a phonon-number measurement of a quantum-mesoscopic-mechanical oscillator

We generalize a proposal for detecting single-phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon-number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the read-out oscillator.

Utilizing encoding in scalable linear optics quantum computing

We present a scheme which offers a significant reduction in the resources required to implement linear optics quantum computing. The scheme is a variation of the proposal of Knill, Laflamme and Milburn, and makes use of an incremental approach to the error encoding to boost probability of success.

The Tausk controversy on the foundations of quantum mechanics: Physics, philosophy, and politics

In 1966 the Brazilian physicist Klaus Tausk (b. 1927) circulated a preprint from the International Centre for Theoretical Physics in Trieste, Italy, criticizing Adriana Daneri, Angelo Loinger, and Giovanni Maria Prosperi`s theory of 1962 on the measurement problem in quantum mechanics. A heated controversy ensued between two opposing camps within the orthodox interpretation of quantum theory, represented by Leon Rosenfeld and Eugene P. Wigner. The controversy went well beyond the strictly scientific issues, however, reflecting philosophical and political commitments within the context of the Cold War, the relationship between science in developed and Third World countries, the importance of social skills, and personal idiosyncrasies.

Quantum analysis of the nondegenerate optical parametric oscillator with injected signal

In this paper we study the nondegenerate optical parametric oscillator with injected signal, both analytically and numerically. We develop a perturbation approach which allows us to find approximate analytical solutions, starting from the full equations of motion in the positive-P representation. We demonstrate the regimes of validity of our approximations via comparison with the full stochastic results. We find that, with reasonably low levels of injected signal, the system allows for demonstrations of quantum entanglement and the Einstein-Podolsky-Rosen paradox. In contrast to the normal optical parametric oscillator operating below threshold, these features are demonstrated with relatively intense fields.

EEG-based Brain-Computer Interfaces: An Overview of Basic Concepts and Clinical Applications in Neurorehabilitation

Some patients are no longer able to communicate effectively or even interact with the outside world in ways that most of us take for granted. In the most severe cases, tetraplegic or post-stroke patients are literally `locked in` their bodies, unable to exert any motor control after, for example, a spinal cord injury or a brainstem stroke, requiring alternative methods of communication and control. But we suggest that, in the near future, their brains may offer them a way out. Non-invasive electroencephalogram (EEG)-based brain-computer interfaces (BCD can be characterized by the technique used to measure brain activity and by the way that different brain signals are translated into commands that control an effector (e.g., controlling a computer cursor for word processing and accessing the internet). This review focuses on the basic concepts of EEG-based BC!, the main advances in communication, motor control restoration and the down-regulation of cortical activity, and the mirror neuron system (MNS) in the context of BCI. The latter appears to be relevant for clinical applications in the coming years, particularly for severely limited patients. Hypothetically, MNS could provide a robust way to map neural activity to behavior, representing the high-level information about goals and intentions of these patients. Non-invasive EEG-based BCIs allow brain-derived communication in patients with amyotrophic lateral sclerosis and motor control restoration in patients after spinal cord injury and stroke. Epilepsy and attention deficit and hyperactive disorder patients were able to down-regulate their cortical activity. Given the rapid progression of EEG-based BCI research over the last few years and the swift ascent of computer processing speeds and signal analysis techniques, we suggest that emerging ideas (e.g., MNS in the context of BC!) related to clinical neuro-rehabilitation of severely limited patients will generate viable clinical applications in the near future.

Image reconstruction affects computer tomographic assessment of lung hyperinflation

Objectives: Lung hyperinflation may be assessed by computed tomography (CT). As shown for patients with emphysema, however, CT image reconstruction affects quantification of hyperinflation. We studied the impact of reconstruction parameters on hyperinflation measurements in mechanically ventilated (MV) patients. Design: Observational analysis. Setting: A University hospital-affiliated research Unit. Patients: The patients were MV patients with injured (n = 5) or normal lungs (n = 6), and spontaneously breathing patients (n = 5). Interventions: None. Measurements and results: Eight image series involving 3, 5, 7, and 10 mm slices and standard and sharp filters were reconstructed from identical CT raw data. Hyperinflated (V-hyper), normally (V-normal), poorly (V-poor), and nonaerated (V-non) volumes were calculated by densitometry as percentage of total lung volume (V-total). V-hyper obtained with the sharp filter systematically exceeded that with the standard filter showing a median (interquartile range) increment of 138 (62-272) ml corresponding to approximately 4% of V-total. In contrast, sharp filtering minimally affected the other subvolumes (V-normal, V-poor, V-non, and V-total). Decreasing slice thickness also increased V-hyper significantly. When changing from 10 to 3 mm thickness, V-hyper increased by a median value of 107 (49-252) ml in parallel with a small and inconsistent increment in V-non of 12 (7-16) ml. Conclusions: Reconstruction parameters significantly affect quantitative CT assessment of V-hyper in MV patients. Our observations suggest that sharp filters are inappropriate for this purpose. Thin slices combined with standard filters and more appropriate thresholds (e.g., -950 HU in normal lungs) might improve the detection of V-hyper. Different studies on V-hyper can only be compared if identical reconstruction parameters were used.

Optimal estimation of one-parameter quantum channels

We explore the task of optimal quantum channel identification and in particular, the estimation of a general one-parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.

A comparison of computer-based methods for the determination of onset of muscle contraction using electromyography

Little consensus exists in the literature regarding methods for determination of the onset of electromyographic (EMG) activity. The aim of this study was to compare the relative accuracy of a range of computer-based techniques with respect to EMG onset determined visually by an experienced examiner. Twenty-seven methods were compared which varied in terms of EMG processing (low pass filtering at 10, 50 and 500 Hz), threshold value (1, 2 and 3 SD beyond mean of baseline activity) and the number of samples for which the mean must exceed the defined threshold (20, 50 and 100 ms). Three hundred randomly selected trials of a postural task were evaluated using each technique. The visual determination of EMG onset was found to be highly repeatable between days. Linear regression equations were calculated for the values selected by each computer method which indicated that the onset values selected by the majority of the parameter combinations deviated significantly from the visually derived onset values. Several methods accurately selected the time of onset of EMG activity and are recommended for future use. Copyright (C) 1996 Elsevier Science Ireland Ltd.

Macroscopic test of quantum mechanics versus stochastic electrodynamics

We identify a test of quantum mechanics versus macroscopic local realism in the form of stochastic electrodynamics. The test uses the steady-state triple quadrature correlations of a parametric oscillator below threshold.

Comparison of palmtop-computer-assisted brief cognitive-behavioral treatment to cognitive-behavioral treatment for panic disorder

In the present study, the authors sought to determine whether the efficiency and cost-effectiveness of cognitive-behavioral treatment (CBT) for panic disorder could be improved by adjunctive computer-assisted therapy. Eighteen participants who met Diagnostic and Statistical Manual of Mental Disorders (3rd ed., revised; American Psychiatric Association, 1987) criteria for panic disorder were randomly assigned to a 12-session CBT (CBT12) condition (D. H. Barlow & M. G. Craske, 1989) or to a 4-session computer-assisted CBT (CBT4-CA) condition. Palmtop computers, with a program developed to incorporate basic principles of CBT, were used by CBT4-CA clients whenever they felt anxious or wanted to practice the therapy techniques and were used by all participants as a momentary assessment tool. CBT4-CA clients carried the computer at all times and continued to use it for 8 weeks after termination of therapy. Analyses of clinically significant change showed superiority of CBT12 at posttest on some measures; however, there were no differences at follow-up.

On the construction of integrable closed chains with quantum supersymmetry

We present a general prescription for the construction of integrable one-dimensional systems with closed boundary conditions and quantum supersymmetry.

Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.