Partitioned Density Matrices and Entanglement Correlators

Abstract

The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems 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 comprise 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.

References in corpus (8)

• Entanglement detection
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Decoherence in Crystals of Quantum Molecular Magnets
• Absolutely maximally entangled states of seven qubits do not exist
• Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths
• Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
• Probing strongly hybrid nuclear-electronic states in a model quantum ferromagnet
• A functional approach to soft graviton scattering and BMS charges

Cited by in corpus (3)

• Maximum $N$-body correlations do not in general imply genuine multipartite entanglement
• Excitation density controlled regimes of collective light--matter dynamics
• BBGKY hierarchy for quantum error mitigation