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

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.14401
 arXiv:
 arXiv:2012.14401
 Bibcode:
 2020arXiv201214401B
 Keywords:

 Mathematical Physics;
 81T05 (Primary) 46N50;
 94A17 (Secondary)
 EPrint:
 slight shortening in Sec. 3