Generalized Coherent States, Reproducing Kernels, and Quantum Support Vector Machines. (arXiv:1612.03713v2 [quant-ph] UPDATED) Quantum Physics - Mon, 2017-02-06 05:07

The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that these algorithms when executed on a classical computer do not scale well with the size of the feature space both in terms of data points and dimensionality. One of the most significant limitations of classical algorithms using non-linear kernels is that the kernel function has to be evaluated for all pairs of input feature vectors which themselves may be of substantially high dimension. This can lead to computationally excessive times during training and during the prediction process for a new data point. Here, we propose using both canonical and generalized coherent states to rapidly calculate specific nonlinear kernel functions. The key link will be the reproducing kernel Hilbert space (RKHS) property for SVMs that naturally arise from canonical and generalized coherent states. Specifically, we discuss the fast evaluation of radial kernels through a positive operator valued measure (POVM) on a quantum optical system based on canonical coherent states. A similar procedure may also lead to fast calculations of kernels not usually used in classical algorithms such as those arising from generalized coherent states.

Categories: Journals, Physics

Effects of static and dynamic higher-order optical modes in balanced homodyne readout for future gravitational waves detectors. (arXiv:1612.00743v2 [gr-qc] UPDATED) Quantum Physics - Mon, 2017-02-06 05:07

With the recent discovery of Gravitational waves, marking the start of the new field of GW astronomy, the push for building more sensitive laser-interferometric gravitational wave detectors (GWD) has never been stronger. Balanced homodyne detection (BHD) allows for a quantum noise limited readout of arbitrary light field quadratures, and has therefore been suggested as a vital building block for upgrades to Advanced LIGO and third generation observatories. In terms of the practical implementation of BHD, we develop a full framework for analyzing the static optical high order modes (HOMs) occurring in the BHD paths related to the misalignment or mode matching at the input and output ports of the laser interferometer. We find the effects of HOMs on the quantum noise limited sensitivity is independent of the actual interferometer configuration, e.g. Michelson and Sagnac interferometers are effected in the same way. We show that output misalignment only effects the high frequency part of the quantum noise limited sensitivity. However, at low frequencies, HOMs reduce the interferometer response and the radiation pressure noise by the same amount and hence the quantum noise limited sensitivity is not negatively effected. We show that the input misalignment to the interferometer produces the same effect as output misalignment and additionally decreases the power inside the interferometer. We also analyze dynamic HOM effects, such as beam jitter created by the suspended mirrors of the BHD. Our analyses can be directly applied to any BHD implementation in a future GWD. Moreover, we apply our analytical techniques to the example of the speed meter proof of concept experiment under construction in Glasgow. We find that for our experimental parameters, the performance of our seismic isolation system in the BHD paths is compatible with the design sensitivity of the experiment.

Categories: Journals, Physics

Laser controlled charge-transfer reaction at low temperatures. (arXiv:1611.05544v3 [physics.atom-ph] UPDATED) Quantum Physics - Mon, 2017-02-06 05:07

We study the low-temperature charge transfer reaction between a neutral atom and an ion under the influence of near-resonant laser light. By setting up a multi-channel model with field-dressed states we demonstrate that the reaction rate coefficient can be enhanced by several orders of magnitude with laser intensities of $10^6$ W/cm$^2$ or larger. In addition, depending on laser frequency one can induce a significant enhancement or suppression of the charge-exchange rate coefficient. For our intensities multi-photon processes are not important.

Categories: Journals, Physics

Cryptographic Quantum Bound on Nonlocality. (arXiv:1605.00438v6 [quant-ph] UPDATED) Quantum Physics - Mon, 2017-02-06 05:07

Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and post-quantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for the full identification of the quantum boundaries already for bipartite settings. The nonlocality inequalities such as so-called the Tsirelson inequality are extended to show how such randomness affects the strength of nonlocal correlations. As a result, a relation followed by most of quantum correlations in the simplest Bell scenario is revealed. The extended inequalities reflect the cryptographic principle such that a completely scrambled message cannot carry information.

Categories: Journals, Physics
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