  We explore the quantum-classical crossover of two coupled, identical,
superconducting quantum interference device (SQUID) rings. The motivation for
this work is based on a series of recent papers. In ~[1] we showed that the
entanglement characteristics of chaotic and periodic (entrained) solutions of
the Duffing oscillator differed significantly and that in the classical limit
entanglement was preserved only in the chaotic-like solutions. However, Duffing
oscillators are a highly idealised toy system. Motivated by a wish to explore
more experimentally realisable systems we extended our work in [2,3] to an
analysis of SQUID rings. In [3] we showed that the two systems share a common
feature. That is, when the SQUID ring's trajectories appear to follow (semi)
classical orbits entanglement persists. Our analysis in[3] was restricted to
the quantum state diffusion unravelling of the master equation - representing
unit efficiency heterodyne detection (or ambi-quadrature homodyne detection).
Here we show that very similar behaviour occurs using the quantum jumps
unravelling of the master equation. Quantum jumps represents a discontinuous
photon counting measurement process. Hence, the results presented here imply
that such persistent entanglement is independent of measurement process and
that our results may well be quite general in nature.

Quantum Physics