Hi Wayne,
Sorry to be so abrupt yesterday.
Attractive (and also repulsive) forces are due to the exchange of certain types of particles. Gravitation is due to the exchange of gravitons. This is, of course, related to the amount of mass that an object has. The mass of a particle, hence its gravity, depend on something called the Higgs field and its quantization called the Higgs boson. This is the only part of the Standard Model of particle physics that has not been observed. The hope is that the Large Hadron Collider (LHC) will show a particular interaction that would indicate the existence of Higgs. (Keep your fingers crossed!)
You asked: "is a gravity-like attraction acting specifically between entangled quanta"?
I won't just say no. Entanglement is what Einstein called "Spukhafte Fernwirkung" i.e., "spooky action at a distance". This sort of entanglement is not like a tangled ball of yarn where a tug on one part makes a tug on another. It speaks more to a phase relation between the wave functions that describe two systems. Einstein and his freinds Podalski and Rosen devised what is known as the EPR paradox in an attempt to show that quantum theory is incomplete. Well that didn't work out. It turns out that QM is nonlocal and there is no real paradox. Entanglement is commonplace and there are certainly aspects of it involved in Higgs. So the answer to your question is sort of no. Does that help?
For more on EPR the original paper is:
http://prola.aps.org/abstract/PR/v47/i10/p777_1also:
http://ej.iop.org/links/rbKdhc0Tq/9vSVOyfB2xG_DvKBav5vpA/ej91n6.pdfFor more on exchange forces see:
http://pos.sissa.it//archive/conferences/037/002/EMC2006_002.pdfhttp://upscale.physics.utoronto.ca/PVB/Harrison/HighEnergy/HighEnergy.pdfhttp://hyperphysics.phy-astr.gsu.edu/hbase/forces/exchg.html#c1Dr. R.
