Hi all, This week, Alberto Spalvieri will talk about “Local Operations and Field Mediated Entanglement without a Local Tensor Product Structure”. See below for the abstract. The talk will take place on Thursday at 11:00 in HIT E41.1. Best, Ladina ******* Title: Local Operations and Field Mediated Entanglement without a Local Tensor Product Structure Abstract: Quantum Information Theory (QIT) has become a powerful framework for probing the foundations of quantum mechanics and has found increasing application across physics. In particular, applying QIT to gauge theories, such as electromagnetism and gravity, might offer a promising route toward understanding the quantum nature of spacetime and field interactions. However, such applications face conceptual challenges: gauge constraints prevent the physical Hilbert space from factorizing into a local tensor product structure, challenging the standard definitions of local operations and entanglement. This thesis addresses these issues using a two-dimensional lattice toy model, closely analogous to electromagnetism, that captures key features of infinite-dimensional gauge theories. Building on previous work, we define gauge-invariant local algebras and induce a physically meaningful decomposition of the Hilbert space. This enables us to formulate operationally consistent notions of locality and entanglement, even without a standard tensor product structure. As an application of our framework, we revisit field-mediated entanglement protocols proposed in recent tests of the quantum nature of gravity. We show that our generalized notions of local operations and entanglement extend the applicability of the LOCC theorem (Local Operations and Classical Communication) to gauge theories, demonstrating that such arguments remain valid even without a trivial local decomposition. Our results also offer a concrete operational understanding of entanglement generation in this context and clarify the role of field-matter interactions.