Evaluation of entanglement entropy in high energy elastic scattering

Abstract

Entanglement of the two scattered particles is expected to occur in elastic collisions, even at high energy where they are in competition with inelastic ones. We study how to evaluate quantitatively the corresponding entanglement entropy S EE . For this sake, we regularize the divergences occurring in the formal derivation of S EE using a regularization procedure acting on the two-particle Hilbert space of final states. A quantitative application is performed in proton-proton collisions at collider energies, comparing the results of S EE with two different cut-offs and with a volume-regularization obtained by a prescription fixing the finite twobody Hilbert space volume. A significant entanglement is found which persists even at the highest available energies.

Relative entropy in scattering and the S-matrix bootstrap

“…(2.2) This was considered previously in [3][4][5][6][7] but we will differ from this analysis in certain crucial aspects. The main aspect is that unlike [3][4][5][6][7] we will focus on the B-particles at a fixed anglefor instance consider a finite resolution detector at a fixed angle θ D . Say, we have put such a detector at an angle θ D = α, whose explicit measure we will specify later.…”

“…The σ → 0 conclusion holds in this case as well, i.e., the entanglement entropy goes to infinity. [3][4][5][6][7] considered certain regularizations to obtain the finite part. As we will see below, the dependence on such regularizations does not arise when we consider relative entropy.…”

“…In the simplest scenario of spin-less scattering, the incoming and outgoing states are specified in terms of the momenta of particles. When one computes entanglement entropy, this entails tracing over momentum states [3][4][5][6][7]. This line of questioning in itself is not novel.…”

“…In Section (3), we consider measures of entanglement focusing on relative entropy. In Section (4), we turn to consider specific theories such as type II superstring theory, λφ 4 theory, and chiral perturbation theory. In Section (5), we turn to generalities focusing on relative entropy.…”

Silence of Binary Kerr Black Holes

“…In computing the entanglement from scattering, there are two sources of difficulty. First, the trace over momentum states lead to divergences due to the infinite space-time volume, and introducing a cutoff leads to regulator dependent results (see, e.g., [13,14]). Second, under Lorentz rotations, the spin undergoes Thomas-Wigner rotation and thus one does not have a Lorentz invariant definition of the reduced density matrix [15,16] (see [17] for further discussions).…”