Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics
Abstract
We study the question of how to decompose Hilbert space into a preferred tensorproduct factorization without any preexisting structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasiclassical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately classical trajectories. We present an inprinciple algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. This formalism is relevant to questions in the foundations of quantum mechanics and the emergence of spacetime from quantum entanglement.
 Publication:

Physical Review A
 Pub Date:
 February 2021
 DOI:
 10.1103/PhysRevA.103.022213
 arXiv:
 arXiv:2005.12938
 Bibcode:
 2021PhRvA.103b2213C
 Keywords:

 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 40 pages, 6 figures. v3 contains version accepted by Phys. Rev. A