Identifying whether a mixed quantum state is uniquely determined among all states (UDA) by its local marginals is a basic problem in quantum information theory. We establish necessary and sufficient conditions under which several classes of multipartite mixed states are UDA by theirk-partite marginals. We also prove structural properties based on ranges and marginals, and formulate a recursive procedure for the determination of UDA states. We show that sufficiently high rank rules out unique determination from fixed-order marginals, implying that almost all multipartite mixed states are not UDA from such marginals. Finally, we completely characterize the additivity of bipartite UDA states, three-qubit and several families ofn-qubit product UDA states. These results clarify the boundary between UDA and non-UDA mixed states and provide a framework for local-marginal reconstruction and related certification tasks.

Recently, large reasoning models (LRMs) have demonstrated state-of-the-art performance across a wide range of benchmarks.However, a common challenge for these models is the "overthinking" problem, which leads to excessive reasoning steps and significant computational overhead.Furthermore, the issues with long Chain-of-Thought (CoT) are especially pronounced in smaller models (≤ 3B parameters).Aside from producing excessively verbose "reflection words", they often exhibit repetition and get trapped in unproductive generation loops.Existing solutions typically involve either using flexible reasoning chains as training data or leveraging the model's latent space to bypass intermediate reasoning steps, but none of these methods have considered directly optimizing reasoning trajectories during the sampling phase of training.In our work, we introduce the Multi-Turn Intervention Sampling Framework (MuTIS).Our framework leverages multi-turn interventions to produce concise reasoning chains.It fine-tunes reasoning models through reinforcement learning, demonstrably breaking the accuracy-efficiency trade-off.It also demonstrates strong scalability, exhibiting excellent performance on 7B models.

Episodes of coral bleaching and subsequent mortality due to abnormal ocean warming have happened more frequently in the world's tropical seas. In 2014, a significant level of thermal stress event was predicted by NOAA CRW in the South China Sea(SCS). In this paper, we estimated the thermal stress anomaly and severity based on NOAA CRW HotSpot and Degree Heating Weeks (DHW) products. An ecological survey was also conducted on nine reefs of Xisha Islands in the SCS from June 2 to June 6, where coral reefs suffered serious damage due to the crown-of-thorns starfish outbreaks in 2007. Satellite results suggest that the beginning of thermal stress in 2014 in the SCS was in mid-May while the ending was in mid-September. Satellite seawater temperature anomalies of +1–2.5°C were recorded at a number of locations. Except the southern portion of Nansha Islands, four offshore archipelagoes tend to be all influenced by this significant warming event. At the time of survey, no significant warming event in Xisha Islands was predicted by NOAA CRW, but scattered coral bleaching was found on Yinyu. Besides, coral cover index of scleractinians indicates obvious coral recovery in Xisha Islands since 2007. The effects of thermal stress in 2014 on coral reefs in the SCS deserve to pay attention and need further investigation.