Relative Entropy of Coherent States on General CCR Algebras

Abstract For a subalgebra of generic CCR algebra, we consider the relative entropy between general (not necessarily pure) quasifree state and coherent excitationthereof. We give unified formula for this in terms single-particle modular data. Further, investigate changes along subalgebras arising from an increasing family symplectic subspaces; here convexity (as usually considered Quantum Null Energy Condition) is replaced with lower estimates second derivative, composed “bulk terms” “boundary terms”. Our main assumption that subspaces are differential position , regularity condition generalizes usual notion half-sided inclusions. illustrate our results relevant examples, including thermal states conformal U (1)-current.