Seminarium KMMF "Teoria Dwoistości"

The quantum focusing conjecture (QFC) expresses the idea that semiclassical gravity remains universally attractive. It predicts how the geometry of spacetime constrains quantum information as the available observables are restricted along light-like directions. Its non-gravitational limit leads to the quantum null energy condition (QNEC), which bounds energy in terms of entanglement. QNEC has been proven in algebraic QFT as a statement about the convexity of relative entropy under light-like deformations. After introducing these ideas, I will discuss sandwiched Rényi divergence, a Rényi generalization of relative entropy. I will then sketch our proof of their analogous convexity under light-like deformations. The proof studies half-sided modular inclusions on Haagerup's non-commutative L^p spaces, which I will introduce as needed. If time permits, I will outline a counterexample to a general Rényi quantum focusing conjecture.