It is, but it's not all quite the same kind of "action at a distance." The correlation of wave functions in quantum mechanics happens without intermediaries, and at superluminal velocities. It is "instantaneous" in fact, although that phrase actually has no Lorentz invariant meaning.
For all the clever calculations and speculations scientists make, they still can't tell us the underlying mechanics of how forces act at a distance.
This statement is false.
We understand quite well how forces act at a distance, and quantum teleportation does not involve those mechanisms. Fundamental interactions are mediated through particles called gauge bosons. The gauge particle of the electromagnetic field is the photon. In order for an electric field to exert a force, the charged particles involved exchange photons. There are gauge particles for each of the fundamental interactions: gluons (strong nuclear force) W and Z bosons (weak nuclear force) and gravitons, in addition to photons. There is some controversy about whether gravitons are actually gauge particles; we do not have a quantum theory of gravity.
All of those gauge bosons provide attractions or repulsions at the speed of light.
The correlation of coherent quantum particles has physical consequences, but is not one of those interactions. It is not a "force" and does not occur at light-speed. This is the essence of Einstein's objection to it.
There are gauge particles for each of the fundamental interactions: gluons (strong nuclear force) W and Z bosons (weak nuclear force) and gravitons, in addition to photons. There is some controversy about whether gravitons are actually gauge particles; we do not have a quantum theory of gravity.
That is entirely correct and beautifully slides over the current central mystery; do gravitons exist or is gravity really geometry?
Gravity behaves like a force in that it propagates at lightspeed (unlike the spooky QM stuff) but nothing like a graviton has been detected. Not for want of trying, but it's a hard problem.
Gravitons are an attractive notion because then all the things that look like forces work the same way and there is some hope of wrapping it all up in one equation that is the literal word of God in the original language.
The trouble with all this tidiness is that it breaks down when we start to think about mass and inertia. And when we collect enough mass to have interesting amounts of gravity it appears that thinking about space-time bending instead of an exchange of gravitons might be a more useful model.
What mass/inertia is exactly is of much interest as there are hints in the math that superluminal velocities are possible (actually required) for objects with an imaginary (square root of -1) rest mass, whatever that means.
No we don't. Claiming that bosons are force mediators still doesn't explain the mechanics of attraction or repulsion. There is still action at a distance between bosons and mediated particles. What pulls them? Every time I ask, I get the answer we don't know. The graviton is still speculation. They haven't confirmed it yet. When it comes to gravity, it's one hell of a long pull between fermions. If they do find a HIggs boson, they still won't be able to explain what the fabric is that provides the resistance to acceleration.