The density matrix of a nonrelativistic quantum system, divided into $N$ subsystems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different subsystems are distinguishable, we derive a hierarchy of equations of motion linking the dynamics of all the partitioned density matrices, analogous to the “Schwinger-Dyson” hierarchy in quantum field theory. The special case of a set of $N$ coupled spin-$1/2$ “qubits” is worked out in detail. The equations are then rewritten in terms of a set of “entanglement correlators,” which comprises all the possible correlation functions for the system—this case is worked out for coupled spin systems. The equations of motion for these correlators can be written in terms of a first-order differential equation for an entanglement correlator supervector.

• Received 2 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.062110