Many problems in the experimental estimation of parameters for models can be solved through use of the likelihood ratio test. Applications of the likelihood ratio, with particular attention to photon counting experiments, are discussed. The procedures presented solve a greater range of problems than those currently in use, yet are no more difficult to apply. The procedures are proved analytically, and examples from current problems in astronomy are discussed.

Parameter estimation in astronomy through application of the likelihood ratio. [satellite data analysis techniques

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Philosophical Transactions of the Royal Society of London. for the Year Mdcccxxvii. Part I. Volume Cxvii:355–388, 1827

Spatial correlations between two photons are the key resource in realising many quantum imaging schemes. Measurement of the bi-photon correlation map is typically performed using single-point scanning detectors or single-photon cameras based on charged coupled device (CCD) technology. However, both approaches are limited in speed due to the slow scanning and the low frame rate of CCD-based cameras, resulting in data acquisition times on the order of many hours. Here, we employ a high frame rate, single-photon avalanche diode (SPAD) camera, to measure the spatial joint probability distribution of a bi-photon state produced by spontaneous parametric down-conversion, with statistics taken over 107 frames. Through violation of an Einstein–Podolsky–Rosen criterion by 227 sigmas, we confirm the presence of spatial entanglement between our photon pairs. Furthermore, we certify, in just 140 s, an entanglement dimensionality of 48. Our work demonstrates the potential of SPAD cameras in the rapid characterisation of photonic entanglement, leading the way towards real-time quantum imaging and quantum information processing.

/pdf/imaging-and-certifying-high-dimensional-entanglement-with-a-4gbxi452xp.pdf

Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera

We performed an loophole-free test of Bells inequalities. The probability that local realism is compatible with our results is less than 5.9×10<sup>-9</sup>.

http://absimage.aps.org/image/MAR16/MWS_MAR16-2015-020168.pdf

A Strong Loophole-Free Test of Local Realism

A plethora of applications hinge on a network or an array of sensors to undertake measurement tasks. A rule of thumb for sensing is that a collective measurement taken by $M$ independent sensors can improve the sensitivity by $1/\sqrt{M}$, known as the standard quantum limit (SQL). Quantum resources such as entanglement and squeezed light can be harnessed to surpass the SQL. Distributed quantum sensing is an emerging subject dedicated to investigating the performance gain enabled by entangled states shared by multiple sensors in tackling different measurement problems. This Review formulates distributed quantum sensing from a quantum-information perspective and describes distributed quantum sensing protocols and their experimental demonstrations. The applications enabled by distributed quantum sensing and an outlook for future opportunities will also be discussed.

Distributed quantum sensing

In this work we investigate quantum-enhanced target detection in the presence of large background noise using multidimensional quantum correlations between photon pairs generated through spontaneous parametric down-conversion. Until now similar experiments have only utilized one of the photon pairs' many degrees of freedom such as temporal correlations and photon number correlations. Here, we utilized both temporal and spectral correlations of the photon pairs and achieved over an order of magnitude reduction to the background noise and in turn significant reduction to data acquisition time when compared to utilizing only temporal modes. We believe this work represents an important step in realizing a practical, real-time quantum-enhanced target detection system. The demonstrated technique will also be of importance in many other quantum sensing applications and quantum communications.

/pdf/multidimensional-quantum-enhanced-target-detection-via-4988a5vyrk.pdf

Multidimensional quantum-enhanced target detection via spectrotemporal-correlation measurements

We describe a simple multivariate technique of likelihood ratios for improved discrimination of signal and background in multi-dimensional quantum target detection. The technique combines two independent variables, time difference and summed energy, of a photon pair from the spontaneous parametric downconversion source into an optimal discriminant. The discriminant performance was studied using experimental data and Monte Carlo modeling with clear improvement shown compared to previous techniques. As novel detectors become available, we expect this type of multivariate analysis to become increasingly important in multi-dimensional quantum optics.

/pdf/multivariate-discrimination-in-quantum-target-detection-1bdk7upmhn.pdf

Multivariate discrimination in quantum target detection

We describe a simple multivariate technique of likelihood ratios for improved discrimination of signal and background in multi-dimensional quantum target detection. The technique combines two independent variables, time difference and summed energy, of a photon pair from the spontaneous parametric down-conversion source into an optimal discriminant. The discriminant performance was studied in experimental data and in Monte-Carlo modelling with clear improvement shown compared to previous techniques. As novel detectors become available, we expect this type of multivariate analysis to become increasingly important in multi-dimensional quantum optics.

Steven Ferrante

Papers

Multidimensional quantum-enhanced target detection via spectrotemporal-correlation measurements

Multivariate discrimination in quantum target detection

Multivariate Discrimination in Quantum Target Detection

Multidimensional quantum illumination via direct measurement of spectro-temporal correlations