I am not a physicist.

But I keep hearing that there is actually nothing mysterious about entanglement at all... Something along the lines of:

You post 2 envelopes containing cards in opposite directions, one with a printed letter A, the other card with the letter B.

At one destination, the envelope is opened to reveal the letter A. ... then through some mysterious quantum mechanical connection.... you know that the envelope at the remote destination contains the letter B.

And that's about all there is to entanglement....

Can any physicist confirm?

I'm not a physicist, just a well-read layman, but...

It *is* more mysterious than that, but if you go with the Many Worlds interpretation it's not *much* more mysterious.

Basically, if you entangle letters A and B and send them in opposite directions, you're really creating two universes corresponding to the two possibilities: universe P (A here, B there) and universe Q (B here, A there). If you open the envelope to reveal A, for instance, then that copy of you in universe P now knows they exists in universe P, and likewise for B and Q. But unlike in classical physics, universe P is not *completely* separated from universe Q. P and Q still exist as a single mathematical object, P-plus-Q, and you can manipulate that mathematical object in ways that don't make sense from a classical standpoint.

Basically, it all comes down to one small thing with big consequences. The real world is NOT described by classical probability (real numbers in the range `[0,1]`). Instead, the real world is described by quantum probability (complex numbers obeying `Re[x]^2 + Im[x]^2 = 1`).

As it turns out, "system P-plus-Q has a 50% chance of P and a 50% chance of Q" is really saying "system P-plus-Q lies at a 45deg angle between the P axis and the Q axis". Starting from P-plus-Q, you can rotate 45deg in one direction to get orthogonal P (A always here), or you can rotate 45deg in the opposite direction to get orthogonal Q (B always here), thus deleting the history of whether A or B was "originally" here. (If P and Q were independent universes, this would decrease entropy and thus break the laws of physics.) Even more counterintuitively, you can even rotate P-plus-Q by 15deg to get a 75% chance A is here and a 25% chance B is here (or vice versa, depending on which quadrant the starting angle was in). Circular rotations in 2-dimensional probability space are the thing that makes quantum probability different from classical probability, and thus the thing that makes quantum physics from classical physics.

Classically, A is either *definitely* here or *definitely* there, and until we open the envelope and look we are merely ignorant of which is the case. Classical physics is time-symmetric, and it therefore forbids randomness from being created or destroyed; classical probability actually measures *ignorance of starting conditions*. In a classical world obeying classical rules, you can't start from "50% A-here, 50% B-here" and transform it into "75% A-here, 25% B-here" without cheating. The required operation would be "flip a coin; if B is here and the coin lands heads, swap envelopes", and you can't carry that out without opening the envelope to check if B is here or not. Quantum physics is *also* time-symmetric and *also* forbids the creation and destruction of randomness, but quantum probability (also called "amplitude") is *not* a mere measure of ignorance. In the Many Worlds way of thinking, physics makes many copies of each possible universe, and the quantum amplitude determines how many copies of each universe to make. At 30deg off the P axis, `cos(30deg)^2` = 75% of the copies are copies of universe P, and you experience this as a 75% probability of finding yourself in a universe with "A here, B there".

(Or something like that. It'll probably make more sense once we eliminate time from the equations. At the moment not even Many Worlds can help us wrap our heads around the fact that quantum entanglement works backward the same as it does forward. The equations as they stand today imply that many past-universes containing past-yous have precisely converged to become the present-universe containing present-you.)

One last complication. If the information of A's location spreads to more particles than A and B, then P and Q become more and more different, and as a consequence the quantum probability rules become harder and harder to distinguish from the classical ones. If you open the envelope and learn "A is here", for instance, then P now contains *billions* of particles that are different from Q (at the very least, the particles in your brain that make up your memory) and it now becomes impossible-ish to perform rotations on P-plus-Q, because you would need to find each particle that changed and rotate it individually. (Not truly impossible, but staggeringly impractical in the same sense that freezing a glass of room-temperature water by gripping each molecule individually to make it sit still is staggeringly impractical. And both are impractical for the same reason: entropy.)

When so many particles are involved that we can't merge the universes back together, we call the situation "decoherence", but it's really just "entanglement of too many things to keep track of". Entanglement itself isn't really that special; what's special is limiting the entanglement to a small group of particles that we can keep track of and manipulate as a group.