We consider entanglement measures in 2-2 scattering in quantum field
theories, focusing on relative entropy which distinguishes two different
density matrices. Relative entropy is investigated in several cases
which include \phi^4ϕ4
theory, chiral perturbation theory (\chi PTχPT)
describing pion scattering and dilaton scattering in type II superstring
theory. We derive a high energy bound on the relative entropy using
known bounds on the elastic differential cross-sections in massive QFTs.
In \chi PTχPT,
relative entropy close to threshold has simple expressions in terms of
ratios of scattering lengths. Definite sign properties are found for the
relative entropy which are over and above the usual positivity of
relative entropy in certain cases. We then turn to the recent numerical
investigations of the S-matrix bootstrap in the context of pion
scattering. By imposing these sign constraints and the
\rhoρ
resonance, we find restrictions on the allowed S-matrices. By performing
hypothesis testing using relative entropy, we isolate two sets of
S-matrices living on the boundary which give scattering lengths
comparable to experiments but one of which is far from the 1-loop
\chi PTχPT
Adler zeros. We perform a preliminary analysis to constrain the allowed
space further, using ideas involving positivity inside the extended
Mandelstam region, and other quantum information theoretic measures
based on entanglement in isospin.
Relative entropy in scattering and the S-matrix bootstrap