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Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called “classical shadows,” with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon-number-resolving, and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with high probability, we show that homodyne detection requires order O(N4+1/3) measurements in the worst case, whereas photon-number-resolving and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental analyses of homodyne tomography match closely with our theoretical predictions. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements. 

Abstract The recent observation of high-lying Rydberg states of excitons in semiconductors with relatively high binding energy motivates exploring their applications in quantum nonlinear optics and quantum information processing. Here, we study Rydberg excitation dynamics of a mesoscopic array of excitons to demonstrate its application in simulation of quantum many-body dynamics. We show that the Z 2 -ordered phase can be reached using physical parameters available for cuprous oxide (Cu 2 O) by optimizing driving laser parameters such as duration, intensity, and frequency. In an example, we study the application of our proposed system to solving the maximum independent set problem based on the Rydberg blockade effect. 

The MMTO Adaptive optics exoPlanet characterization System (MAPS) is an ongoing upgrade to the 6.5-meter MMT Observatory on Mount Hopkins in Arizona. MAPS includes an upgraded adaptive secondary mirror (ASM), upgrades to the ARIES spectrograph, and a new AO system containing both an optical and near-infrared (NIR; 0.9-1.8 μm) pyramid wavefront sensor (PyWFS). The NIR PyWFS will utilize an IR-optimized double pyramid coupled with a SAPHIRA detector: a low-read noise electron Avalanche Photodiode (eAPD) array. This NIR PyWFS will improve MAPS's sky coverage by an order of magnitude by allowing redder guide stars (e.g. K & M-dwarfs or highly obscured stars in the Galactic plane) to be used. To date, the custom designed cryogenic SAPHIRA camera has been fully characterized and can reach sub-electron read noise at high avalanche gain. In order to test the performance of the camera in a closed-loop environment prior to delivery to the observatory, an AO testbed was designed and constructed. In addition to testing the SAPHIRA's performance, the testbed will be used to test and further develop the proposed on-sky calibration procedure for MMTO's ASM. We will report on the anticipated performance improvements from our NIR PyWFS, the SAPHIRA's closed-loop performance on our testbed, and the status of our ASM calibration procedure. 

Abstract Pulsar timing array observations have found evidence for an isotropic gravitational-wave background with the Hellings–Downs angular correlations between pulsar pairs. This interpretation hinges on the measured shape of the angular correlations, which is predominantly quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipolesℓ≥ 2, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and nonzero at the ∼95% confidence level and a Bayes factor of 200. When we include multipolesℓ≤ 1, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz, which has also been noted in previous analyses of the NANOGrav 15 yr data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations. 

The MMT Adaptive optics exoPlanet characterization System (MAPS) is an exoplanet characterization program that encompasses instrument development, observational science, and education. The instrument we are developing for the 6.5m MMT observatory is multi-faceted, including a refurbished 336-actuator adaptive secondary mirror (ASM); two pyramid wavefront sensors (PyWFS's); a 1-kHz adaptive optics (AO) control loop; a high-resolution and long-wavelength upgrade to the Arizona infraRed Imager and Echelle Spectrograph (ARIES); and a new-AO-optimized upgrade to the MMT-sensitive polarimeter (MMT-Pol). With the completed MAPS instrument, we will execute a 60-night science program to characterize the atmospheric composition and dynamics of ~50-100 planets around other stars. The project is approaching first light, anticipated for Summer/Fall of 2022. With the electrical and optical tests complete and passing the review milestone for the ASM's development, it is currently being tuned. The PyWFS's are being built and integrated in their respective labs: the visible-light PyWFS at the University of Arizona (UA), and the infrared PyWFS at the University of Toronto (UT). The top-level AO control software is being developed at UA, with an on-sky calibration algorithm being developed at UT. ARIES development continues at UA, and MMT-Pol development is at the University of Minnesota. The science and education programs are in planning and preparation. We will present the design and development of the entire MAPS instrument and project, including an overview of lab results and next steps.