Entanglement and Nonunitary Evolution

TL;DR

The paper investigates whether tracing over inaccessible regions in an entangled quantum system induces nonunitary evolution for an external observer. It develops a general master-equation framework (Nakajima-Zwanzig) for a reduced density matrix and provides a concrete lattice construction of a collapsing spherical shell in a free field to demonstrate time-dependent eigenvalues of the exterior density matrix. The authors show, via explicit calculation and numerics, that Tr(rho_out^2) becomes time-dependent when the interior is traced, signaling apparent nonunitarity. They connect these findings to entanglement entropy with area scaling and discuss implications for black hole physics, arguing that global unitary evolution is preserved while the exterior description can be nonunitary due to horizon-induced tracing.

Abstract

We consider a collapsing relativistic spherical shell for a free quantum field. Once the center of the wavefunction of the shell passes a certain radius R, the degrees of freedom inside R are traced over. We show that an observer outside this region will determine that the evolution of the system is nonunitary. We argue that this phenomenon is generic to entangled systems, and discuss a possible relation to black hole physics.