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1. Emergent complex quantum networks in continuous-variables non-Gaussian states

   Mattia Walschaers, Nicolas Treps (July 2021, ArXivorg)

   Large multipartite quantum systems tend to rapidly reach extraordinary levels of complexity as their number of constituents and entanglement links grow. Here we use complex network theory to study a class of continuous variables quantum states that present both multipartite entanglement and non-Gaussian statistics. In particular, the states are built from an initial imprinted cluster state created via Gaussian entangling operations according to a complex network structure. To go beyond states that can be easily simulated via classical computers we engender non-Gaussian statistics via multiple photon subtraction operations. We then use typical networks measures, the degree and clustering, to characterize the emergent complex network of photon-number correlations after photon subtractions. We show that, in contrast to regular clusters, in the case of imprinted complex network structures the emergent correlations are strongly affected by photon subtraction. On the one hand, we unveil that photon subtraction universally increases the average photon-number correlations, regardless of the imprinted network structure. On the other hand, we show that the shape of the distributions in the emergent networks after subtraction is greatly influenced by the structure of the imprinted network, as witnessed by their higher-moments. Thus for the field of network theory, we introduce a new class of networks to study. At the same time for the field of continuous variable quantum states, this work presents a new set of practical tools to benchmark systems of increasing complexity. 

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2. A Simulator of Atom-Atom Entanglement with Atomic Ensembles and Quantum Optics

   https://doi.org/10.1109/QCE57702.2023.00143  

   Zhou, Ruilin; Lai, Xuanying; Gan, Yuhang; Obraczka, Katia; Du, Shengwang; Qian, Chen (September 2023, IEEE)

   One fundamental goal of quantum networks is to provide node-to-node entanglement distribution. In this work, we develop a simulator, called A 2 Tango, for entanglement generation between two remote atom-ensemble nodes in a quantum network following Briegel, Dur, Cirac and Zoller (BDCZ) protocol. We encode quantum information to the two spatial modes of local atomic-ensemble spin waves and polarization states of single photons. The basic operations include atom-photon entanglement generation, quantum memory write-read operations, two-photon Bell-state measurement, and quantum state tomography. We model multi-photon events during the local excitation and propagation to account for their induced error in entanglement generation and distribution. We investigate the entanglement generation rate and fidelity as functions of the parameters which are realizable in experiments. Our work improves the open-sourced SeQUeNCe simulator and inspires the development of future quantum networks. 

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3. Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state

   https://doi.org/10.22331/q-2022-07-20-769  

   Eaton, Miller; González-Arciniegas, Carlos; Alexander, Rafael N.; Menicucci, Nicolas C.; Pfister, Olivier (July 2022, Quantum)

   We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schrödinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. This method stabilizes cat states against Gaussian noise and perpetuates non-Gaussianity within the cluster. We show that existing protocols for breeding cat states can be embedded into cluster state processing using PhANTM. 

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4. Simulating lossy Gaussian boson sampling with matrix-product operators

   https://doi.org/10.1103/PhysRevA.108.052604  

   Liu, Minzhao; Oh, Changhun; Liu, Junyu; Jiang, Liang; Alexeev, Yuri (November 2023, Physical Review A)

   Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the Nout ~ \sqrt(N) scaling of the number of surviving photons Nout in the number of input photons N. We numerically verify this result using a tensor network algorithm with U(1) symmetry, and we overcome previous challenges due to the large local Hilbert-space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks. 

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5. Determination of the asymptotic limits of adaptive photon counting measurements for coherent-state optical phase estimation

   https://doi.org/10.1038/s41534-022-00601-8  

   Rodríguez-García, M. A.; DiMario, M. T.; Barberis-Blostein, P.; Becerra, F. E. (December 2022, npj Quantum Information)

   Abstract Physical realizations of the canonical phase measurement for the optical phase are unknown. Single-shot phase estimation, which aims to determine the phase of an optical field in a single shot, is critical in quantum information processing and metrology. Here we present a family of strategies for single-shot phase estimation of coherent states based on adaptive non-Gaussian, photon counting, measurements with coherent displacements that maximize information gain as the measurement progresses, which have higher sensitivities over the best known adaptive Gaussian strategies. To gain understanding about their fundamental characteristics and demonstrate their superior performance, we develop a comprehensive statistical analysis based on Bayesian optimal design of experiments, which provides a natural description of these non-Gaussian strategies. This mathematical framework, together with numerical analysis and Monte Carlo methods, allows us to determine the asymptotic limits in sensitivity of strategies based on photon counting designed to maximize information gain, which up to now had been a challenging problem. Moreover, we show that these non-Gaussian phase estimation strategies have the same functional form as the canonical phase measurement in the asymptotic limit differing only by a scaling factor, thus providing the highest sensitivity among physically-realizable measurements for single-shot phase estimation of coherent states known to date. This work shines light into the potential of optimized non-Gaussian measurements based on photon counting for optical quantum metrology and phase estimation. 

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