探索全球前沿学术脉络

Unveiling Hierarchical Invariants in Multiphoton Linear Optics

arXiv:2506.12857v2 Announce Type: replace Abstract: Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.

Measuring Whether LLM Tutors Teach or Solve: A Diagnostic for Educational Impact

Large language models are increasingly proposed as educational tutors, yet stronger task-solving ability does not necessarily imply stronger learning support. Motivated by recent calls to measure the social impact of NLP systems in practice, we study whether public LLM tutoring benchmarks distinguish learning-supportive behavior from mere answer production. We propose a lightweight diagnostic based on the gap between solving-oriented and pedagogy-oriented benchmark performance. Using public MathTutorBench leaderboard results, we show that these dimensions are only partially aligned: across eight publicly reported models, the correlation between solving and pedagogy composites is 0.421, and several models shift meaningfully in rank when evaluation moves from solving to pedagogy. We then analyze the public TutorBench sample and show that agency-relevant behaviors are explicitly encoded in benchmark rubrics, especially in active-learning settings that reward guiding questions, calibrated hints, and non-disclosive scaffolding. Together, these findings suggest that educational-impact evaluation should not treat task success as a sufficient proxy for learning support. We argue that public tutoring benchmarks can better support positive-impact evaluation by reporting solving-oriented and pedagogy-oriented scores separately and by making disclosure-sensitive, student-agency-preserving criteria more explicit.