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arXiv · 1808.01054

Partitioned Density Matrices and Entanglement Correlators

Timothy Cox·Philip C. E. Stamp
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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.

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Timothy Cox, Philip C. E. Stamp. 2018-08-03. Partitioned Density Matrices and Entanglement Correlators. https://doi.org/10.1103/physreva.98.062110

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