Entanglement formation in continuous-variable random quantum networks

Entanglement is not only important for understanding the fundamental properties of many-body systems, but also the crucial resource enabling quantum advantages in practical information processing tasks. While previous works on entanglement formation and networking focus on discrete-variable systems, light---as the only travelling carrier of quantum information in a network---is bosonic and thus requires a continuous-variable description in general. In this work, we extend the study to continuous-variable quantum networks. By mapping the ensemble-averaged entanglement dynamics on an arbitrary network to a random-walk process on a graph, we are able to exactly solve the entanglement dynamics and reveal unique phenomena. We identify squeezing as the source of entanglement generation, which triggers a diffusive spread of entanglement with a parabolic light cone. The entanglement distribution is directly connected to the probability distribution of the random walk, while the scrambling time is determined by the mixing time of the random walk. The dynamics of bipartite entanglement is determined by the boundary of the bipartition; An operational witness of multipartite entanglement, based on advantages in sensing tasks, is introduced to characterize the multipartite entanglement growth. A surprising linear superposition law in the entanglement growth is predicted by the theory and numerically verified, when the squeezers are sparse in space-time, despite the nonlinear nature of the entanglement dynamics. We also give exact solution to the equilibrium entanglement distribution (Page curves), including its fluctuations, and found various shapes dependent on the average squeezing density and strength.Comment: 15+3+2 pages, 24 figure

On Compositional Data Modeling and Its Biomedical Applications

Compositional data occur naturally in biomedical studies which investigate changes in the proportions of various components of a combined medical measurement. The statistical method to analyze this type of data is underdeveloped. Currently the multivariate logitnormal model seems to be the only model routinely used in analyzing compositional data, and its application is mainly in geology and has yet to be known to the biomedical elds. In this dissertation, we propose the multivariate simplex model as an alternative method of modeling compositional data, either cross-sectional or longitudinal and develop statistical methods to analyze such data. We suggest three approaches to making a fair comparison between the multivariate simplex models and the multivariate logit-normal models. The simulations indicate that our proposed multivariate simplex models often outperform the multivariate logit-normal models

Multivariate Linear and Non-Linear Causality Tests with Applications

Master'sMASTER OF SCIENC

Entangling remote microwave quantum computers with hybrid entanglement swap and variational distillation

Superconducting microwave circuits with Josephson junctions are a major platform for quantum computing. To unleash their full capabilities, the cooperative operation of multiple microwave superconducting circuits is required. Therefore, designing an efficient protocol to distribute microwave entanglement remotely becomes a crucial open problem. Here, we propose a continuous-variable entanglement-swap approach based on optical-microwave entanglement generation, which can boost the ultimate rate by two orders of magnitude at state-of-the-art parameter region, compared with traditional approaches. We further empower the protocol with a hybrid variational entanglement distillation component to provide huge advantage in the infidelity-versus-success-probability trade-off. Our protocol can be realized with near-term device performance, and is robust against non-perfections such as optical loss and noise. Therefore, our work provides a practical method to realize efficient quantum links for superconducting microwave quantum computers.Comment: 5+10 pages, 4+10 figure

Optimal entanglement-assisted electromagnetic sensing and communication in the presence of noise

High time-bandwidth product signal and idler pulses comprised of independent identically distributed two-mode squeezed vacuum (TMSV) states are readily produced by spontaneous parametric downconversion. These pulses are virtually unique among entangled states in that they offer quantum performance advantages -- over their best classical-state competitors -- in scenarios whose loss and noise break their initial entanglement. Broadband TMSV states' quantum advantage derives from its signal and idler having a strongly nonclassical phase-sensitive cross correlation, which leads to information bearing signatures in lossy, noisy scenarios stronger than what can be obtained from classical-state systems of the same transmitted energy. Previous broadband TMSV receiver architectures focused on converting phase-sensitive cross correlation into phase-insensitive cross correlation, which can be measured in second-order interference. In general, however, these receivers fail to deliver broadband TMSV states' full quantum advantage, even if they are implemented with ideal equipment. This paper introduces the correlation-to-displacement receiver -- a new architecture comprised of a correlation-to-displacement converter, a programmable mode selector, and a coherent-state information extractor -- that can be configured to achieve quantum optimal performance in known sensing and communication protocols for which broadband TMSV provides quantum advantage that is robust against entanglement-breaking loss and noise.Comment: 14+17 pages, 12+9 figures. A preliminary version of the manuscript can be found in arXiv:2207.0660

Dynamical phase transition in quantum neural networks with large depth

Understanding the training dynamics of quantum neural networks is a fundamental task in quantum information science with wide impact in physics, chemistry and machine learning. In this work, we show that the late-time training dynamics of quantum neural networks can be described by the generalized Lotka-Volterra equations, which lead to a dynamical phase transition. When the targeted value of cost function crosses the minimum achievable value from above to below, the dynamics evolve from a frozen-kernel phase to a frozen-error phase, showing a duality between the quantum neural tangent kernel and the total error. In both phases, the convergence towards the fixed point is exponential, while at the critical point becomes polynomial. Via mapping the Hessian of the training dynamics to a Hamiltonian in the imaginary time, we reveal the nature of the phase transition to be second-order with the exponent $\nu=1$, where scale invariance and closing gap are observed at critical point. We also provide a non-perturbative analytical theory to explain the phase transition via a restricted Haar ensemble at late time, when the output state approaches the steady state. The theory findings are verified experimentally on IBM quantum devices.Comment: 11+35 pages, comments are welcome

Epigenetic Landscape in Leukemia and Its Impact on Antileukemia Therapeutics

Epigenomic landscape mapping in leukemia cells supports germ line mutation studies to understand pathogenicity and treatment plans. The differential regulation of gene expression and heterogeneity between cell types during hematopoiesis and leukemia development is important in understanding oncogenesis. Oncogenesis in leukemia occurs at both genomic and epigenomic levels in order for hematological cells to evade lineage commitment. To ensure that therapies target the entire malignancy, it is important to consider the regulatory network that drives malignancy caused by mutations. Therapies tailored to respond to a patient-specific epigenetic landscape have the potential to minimize risk in administering chemotherapies that may not work. In this chapter, a focused study on childhood acute lymphoblastic leukemia (ALL) will be used as an example of the current research in the field of epigenetics in leukemia and the impact it carries on our understanding of the disease and treatment plans

Investigation of the clinical features and therapeutic methods for the management of inflammatory lacrimal punctum diseases

Purpose: To establish if there are different classes of inflammatory lacrimal punctum diseases (ILPDs) and to examine the various strategies by which they can be managed therapeutically.Methods: Two hundred and fifty nine (259) patients with inflammatory punctum lacrimal disease were identified and used as subjects for this study. Each patient was carefully examined for evidence of morphology of lacrimal punctum which was confirmed mainly by lacrimal duct flushing and probing. Appropriate therapeutic managements were adopted for patients with other inflammatory conditions besides ILPD. The clinical effects of the various therapeutic strategies were documented. .Results: Eighty-seven (87) patients out of the 259 (32.53 %) suffered from acute or chronic conjunctivitis while 66 patients (5.61 %) suffered from inflammatory lacrimal passage diseases. Patients with both conjunctivitis and lacrimal passage inflammation, patients with dry-eye symptoms, patients with just one of the conditions, and patients with mere evidence of superior punctalacrimalis represented 13.15, 14.19, 14.53, and 33.91 %, respectively. Mere evidence of inferior punctalacrimalis, and presence of acute inflammation were seen in 48.76 and 13.49 % of the 259 patients, respectively, while those with chronic inflammation lasting for 2.97 ± 0.13 years, comprised 86.51 %. Antibiotic eye drops were used for acute inflammation, while chronic inflammation was treated with antibiotic eye drops, lacrimal punctum expansion, pus elimination, and punctum-sparing canaliculotomy. Both therapeutic methods produced satisfactory curative effects.Conclusion: The results show that satisfactory therapy of lacrimal punctum inflammation can be achieved if the right therapeutic agents and procedures are adopted based on clinical characteristics of the ILPD manifesting in the patient.Keywords: Lacrimal punctum, Inflammatory disease, Conjunctivitis, Dry-eye symptom