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We determine the resource scaling of machine learning-based quantum state reconstruction methods, in terms of inference and training, for systems of up to four qubits when constrained to pure states. Further, we examine system performance in the low-count regime, likely to be encountered in the tomography of high-dimensional systems. Finally, we implement our quantum state reconstruction method on an IBM Q quantum computer, and compare against both unconstrained and constrained MLE state reconstruction., 9 pages

We derive the Dirichlet concentration parameters for mixtures of Haar-random pure states that recover mean purities equal to standard measures, demonstrating how tailored distributions attain appreciable performance advantages in machine-learning-based and Bayesian quantum state reconstruction.

The quantum Zeno effect reveals that continuous observation of a quantum system can significantly alter its evolution. Here, we present a method for establishing polarization entanglement between two initially unentangled photons in coupled waveguides via the quantum Zeno effect. We support our analytical investigation with numerical simulations of the underlying Schrodinger equation describing the system. Further, we extend our technique to three coupled waveguides in a planar configuration and determine the parameters required to generate three-qubit W-states. In contrast to existing schemes based on a vacuum and single-photon encoding, the polarization encoding in our approach is compatible with quantum information protocols that remove photon loss through post-selection. Our findings offer a powerful quantum state engineering approach for photonic quantum information technologies.

Evanescent waves are central to many technologies such as near-field imaging that beats the diffraction limit and plasmonic devices. Frustrated total internal reflection (FTIR) is an experimental method commonly used to study evanescent waves. In this paper, we shape the incident beam of the FTIR process with a Mach-Zehnder interferometer and measure light transmittance while varying the path length difference and interferometric visibility. Our results show that the transmittance varies with the path length difference and, thus, the intensity distribution of the shaped beam. Experiment and finite element method simulation produce results that agree. We also show, through simulations, that the transmittance can be controlled via other methods of beam shaping. Our work provides a proof-of-concept demonstration of the coherent control of the FTIR process, which could lead to advancements in numerous applications of evanescent waves and FTIR., Comment: 11 pages, 6 figures, 1 table

We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert--Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert--Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert--Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert--Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert--Schmidt distributed states for various experimental conditions., 16 pages, 15 figures

In this presentation, we show the efficacy of neural networks in reducing classical resources required for quantum state estimation. The developed methods achieve near-unity fidelities in reconstructed density matrices, and outperform Stokes reconstruction in a wide variety of scenarios.

We examine the efficacy of machine learning in reducing the bit-error rate of a free-space optical ON-OFF keying communication scheme in the presence of experimentally generated atmospheric effects: turbulence and thermal background radiation.

We present theoretical methods for simulating the evolution of quantum Gibbs states using classical light and epsilon-near-zero materials, which allow for easy measure- ment of the statistical information of the simulated system.

We present an experimental violation of the Leggett-Garg inequality in classical optics using only the polarization degree-of-freedom of a laser beam. Our results show maximum violations of the Leggett-Garg inequality.

We study the efficacy of deep learning-based quantum state reconstruction methods with respect to inference and training, and then implement the reconstruction technique on an IBM quantum computer.

In contrast to Bell's inequalities which test the correlations between multiple spatially separated systems, the Leggett-Garg inequalities test the temporal correlations between measurements of a single system. We experimentally demonstrate the violation of the Leggett-Garg inequality in a classical optical system using only the polarization degree-of-freedom of a laser beam. Our results show maximal violations of the Leggett-Garg inequality., 4 pages. Full manuscript

Phase-sensitive nonlinear gain processes have been implemented as noise-reduced optical amplifiers, which have the potential to achieve signal-to-noise ratios beyond the classical limit. We experimentally demonstrate a novel phase-sensitive four-wave mixing amplification process in a single atomic vapor cell with only two input frequencies and two input vacuum modes. The amount of phase sensitivity depends on the power ratio between the inserted probes as well as on the input frequency of the probes. We find that, for certain phase values, the intensity noise of an output mode is lower than that of its phase-insensitive counterpart.

We present mathematical methods, based on convex optimization, for correcting non-physical coherency matrices measured in polarimetry. We also develop the method for recovering the coherency matrices corresponding to the smallest and largest values of the degree of polarization given the experimental data and a specified tolerance. We use experimental non-physical results obtained with the standard polarimetry scheme and a commercial polarimeter to illustrate these methods. Our techniques are applied in post-processing, which complements other experimental methods for robust polarimetry., Comment: 15 pages and 6 figures. Comparison with other methods added

Spatial modes of light constitute valuable resources for a variety of quantum technologies ranging from quantum communication and quantum imaging to remote sensing. Nevertheless, their vulnerabilities to phase distortions, induced by random media, impose significant limitations on the realistic implementation of numerous quantum-photonic technologies. Unfortunately, this problem is exacerbated at the single-photon level. Over the last two decades, this challenging problem has been tackled through conventional schemes that utilize optical nonlinearities, quantum correlations, and adaptive optics. In this article, we exploit the self-learning and self-evolving features of artificial neural networks to correct the complex spatial profile of distorted Laguerre-Gaussian modes at the single-photon level. Furthermore, we demonstrate the possibility of boosting the performance of an optical communication protocol through the spatial mode correction of single photons using machine learning. Our results have important implications for real-time turbulence correction of structured photons and single-photon images., Comment: 7 pages, 4 figures

We design a deep learning assisted end to end free-space optical ON-OFF Keying communications system, and demonstrate its efficacy in significantly lowering the bit error rate, while requiring no knowledge of the channel state information.

We present a mathematical method of correcting non-physical results from polarimetry measurements based on convex optimization. We show the experimental nonphysical measurements and the corresponding corrected results.

We use a deep learning neural network to successfully indicate when an eavesdropper is present in a free-space optics ON-OFF keying communication scheme, in which the bit stream has passed through turbulence.

Reconstruction of two-qubit systems typically performed using 36 coincidence measurements. We trained an ensemble of CNN & XGBoost ML models, employed imputation to demonstrate high-fidelity state estimation when multiple measurements are missing.

Realistic free-space optical communications systems suffer from turbulent propagation of light through the atmosphere and detector noise at the receiver, which can significantly degrade the optical mode quality of the received state, increase cross-talk between modes, and correspondingly increase the symbol error ratio (SER) of the system. In order to overcome these obstacles, we develop a state-of-the-art generative machine learning (GML) and convolutional neural network (CNN) system in combination, and demonstrate its efficacy in a free-space optical (FSO) communications setting. The system corrects for the distortion effects due to turbulence and reduces detector noise, resulting in significantly lowered SERs and cross-talk at the output of the receiver, while requiring no feedback. This scheme is straightforward to scale, and may provide a concrete and cost effective technique to establishing long range classical and quantum communication links in the near future., 9 pages, 5 figures

In this work we demonstrate the efficacy of neural networks in the characterization of dispersive media. We also develop a neural network to make predictions for input probe pulses which propagate through a nonlinear dispersive medium, which may be applied to predicting optimal pulse shapes for a desired output. The setup requires only a single pulse for the probe, providing considerable simplification of the current method of dispersion characterization that requires frequency scanning across the entirety of the gain and absorption features. We show that the trained networks are able to predict pulse profiles as well as dispersive features that are nearly identical to their experimental counterparts. We anticipate that the use of machine learning in conjunction with optical communication and sensing methods, both classical and quantum, can provide signal enhancement and experimental simplifications even in the face of highly complex, layered nonlinear light-matter interactions., Comment: 7 pages, 5 figures

Turbulence imposes major limitations to free-space protocols for optical communication and cryptography. Here, we report our progress on the experimental demonstration of turbulence correction of Laguerre-Gauss modes using artificial neural networks.

We design a state-of-the-art generative machine learning system that mitigates the distortion effects of turbulence and reduces detector noise, which results in remarkably lowered bit error ratios, while requiring no feedback.

We present a dual-pump setup for generating tripartite entanglement using four-wave mixing in warm atomic vapor. We derive the output state for vacuum inputs and show that this state is genuine tripartite entangled.

We demonstrate an unseeded multimode four-wave-mixing process in hot $^{85}\mathrm{Rb}$ vapor using two pump beams of the same frequency that cross at a small angle. This results in the simultaneous fulfillment of multiple phase-matching conditions that reinforce one another to produce four intensity-stabilized bright output modes at two different frequencies. Each generated photon is directly correlated to exactly two others, resulting in the preferred four-mode output, in contrast to other multimode four-wave-mixing experiments. This provides significant insight into the optimal configuration of the output multimode squeezed and entangled states generated in such four-wave-mixing systems. We examine the power, temperature, and frequency dependence of this output and compare it to the conical four-wave-mixing emission from a single pump beam. The generated beams are spatially separated, allowing a natural distribution for potential use in quantum communication and secret-sharing protocols.

We experimentally investigate the propagation of optical pulses through a fast-light medium with competing absorption and gain. The combination of strong absorption and optical amplification in a potassium-based four-wave mixing process results in pulse peak advancements up to $88\%$ of the input pulse width, more than $35 \times$ that which is achievable without competing absorption. We show that the enhancement occurs even when the total gain of the four-wave mixer is unity, thereby rendering the medium transparent. By varying the pulse width, we observe a transition between fast and slow light, and show that fast light is optimized for large pulse widths., Comment: Comments are very welcomed. \copyright 2018 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved

Optical parametric amplifiers (OPAs) play a fundamental role in the generation of quantum correlation for quantum information processing and quantum metrology. In order to increase the communication fidelity of the quantum information protocol and the measurement precision of quantum metrology, it requires a high degree of quantum correlation. In this Rapid Communication we report a feedback optical parametric amplifier that employs a four-wave mixing (FWM) process as the underlying OPA and a beam splitter as the feedback controller. We first construct a theoretical model for this feedback-based FWM process and experimentally study the effect of the feedback control on the quantum properties of the system. Specifically, we find that the quantum correlation between the output fields can be enhanced by tuning the strength of the feedback.

We design an optical feedback network making use of machine learning techniques and demonstrate via simulations its ability to correct for the effects of turbulent propagation on optical modes. This artificial neural network scheme only relies on measuring the intensity profile of the distorted modes, making the approach simple and robust. The network results in the generation of various mode profiles at the transmitter that, after propagation through turbulence, closely resemble the desired target mode. The corrected optical mode profiles at the receiver are found to be nearly identical to the desired profiles, with near-zero mean square error indices. We are hopeful that the present results combining the fields of machine learning and optical communications will greatly enhance the robustness of free-space optical links., Comment: 4 pages, 4 figures, 1 table

Information transfer rates in optical communications may be dramatically increased by making use of spatially non-Gaussian states of light. Here we demonstrate the ability of deep neural networks to classify numerically-generated, noisy Laguerre-Gauss modes of up to 100 quanta of orbital angular momentum with near-unity fidelity. The scheme relies only on the intensity profile of the detected modes, allowing for considerable simplification of current measurement schemes required to sort the states containing increasing degrees of orbital angular momentum. We also present results that show the strength of deep neural networks in the classification of experimental superpositions of Laguerre-Gauss modes when the networks are trained solely using simulated images. It is anticipated that these results will allow for an enhancement of current optical communications technologies., Comment: 10 pages, 15 figures. \copyright 2018 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved

We study the average coincidence-count signal at the output of a two-mode squeezing device with $|N\rangle\otimes|\alpha\rangle$ as the two input modes. We show that the input photon-number can be resolved from the average coincidence counts. In particular, we show jumps in the average coincidence-count signal as a function of input photon-number $N$. Therefore, we propose that such a device may be deployed as photon-number-resolving detector at room temperature with high efficiency., Comment: 9 pages, 11 figures