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We study quantum state certification using unentangled quantum measurements, namely measurements which operate only on one copy of the state at a time. When there is a common source of randomness available and the unentangled measurements are chosen based on this randomness, prior work has shown that copies are necessary and sufficient. We show a separation between algorithms with and without randomness. We develop a lower bound framework for both fixed and randomized measurements that relates the hardness of testing to the well-established Lüders rule. More precisely, we obtain lower bounds for randomized and fixed schemes as a function of the eigenvalues of the Lüders channel which characterizes one possible post-measurement state transformation. 

Chemical reaction data has existed and still largely exists in unstructured forms. But curating such information into datasets suitable for tasks such as yield and reaction outcome prediction is impractical via manual curation and not possible to automate through programmatic means alone. Large language models (LLMs) have emerged as potent tools, showcasing remarkable capabilities in processing textual information and therefore could be extremely useful in automating this process. To address the challenge of unstructured data, we manually curated a dataset of structured chemical reaction data to fine-tune and evaluate LLMs. We propose a paradigm that leverages prompt-tuning, fine-tuning techniques, and a verifier to check the extracted information. We evaluate the capabilities of various LLMs, including LLAMA-2 and GPT models with different parameter counts, on the data extraction task. Our results show that prompt tuning of GPT-4 yields the best accuracy and evaluation results. Fine-tuning LLAMA-2 models with hundreds of samples does enable them and organize scientific material according to user-defined schemas better though. This workflow shows an adaptable approach for chemical reaction data extraction but also highlights the challenges associated with nuance in chemical information. We open-sourced our code at GitHub.