Mutual information superadditivity and unitarity bounds

Abstract

We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.

v2. Fixed typos, added references, and expanded discussion on conformal block decomposition of the mutual information

References in corpus (2)

• Entropy on a null surface for interacting quantum field theories and the Bousso bound
• Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres

Cited by in corpus (7)

• A universal feature of charged entanglement entropy
• Tripartite information at long distances
• Mutual Information of Generalized Free Fields
• Conformal bounds in three dimensions from entanglement entropy
• Aspects of N-partite information in conformal field theories
• Mutual information from modular flow in CFTs
• Shape dependence of mutual information in the OPE limit: linear responses