Entanglement is more than the coin thing, and less than the FTL thing. Which can make it pretty frustrating to explain, because people just keep oscillating between "Oh, then it has instantaneous observable effects?" and "Oh, then it's just agreeing on a value ahead of time?" instead of stopping at the right point.

Imagine that I give you a magic piece of paper with two binary digits (00/01/10/11) on it. I also keep such a paper for myself. If we both start by looking at our first digits then those will mysteriosly match, but if we then look at our second digits they will have just a 50% chance of matching. However, if we both start by looking at the last digits, then those will match, and our first digits will have a 50% chance of matching. If you and I start by looking at different digits, then the digits we read are just standard random bits.

The cool thing about this is that our magic paper will also work instantly even if we are lightyears apart. However, if you decide to look at the last digit and you see a 1, then that tells you nothing about me or which digits (if any) I have looked at, so I can't send you a message with this paper.

Ah, so if I understand correctly, you could detect message eavesdropping as follows:

1. We agree ahead of time to always observe the first digit of magic papers first.

2. I send you a message that includes eavesdropping-detecting magic pieces of paper

3. We then compare what you measured as first digits to what I measured as first digits

4. If the digits do not match, it means someone eavesdropped on the magic pieces of paper I sent and observed the wrong digits first.

But then aren't we back to the same secret distribution problem, where the secret is which digit we should observe first on magic papers?

As you point out, that protocol is flawed.

Here is a protocol that works (BB84):

Needed:

* A way for Alice to communicate (classically) with Bob that can be read by Eve, but CANNOT be manipulated by Eve.

* A way for Alice to send magic paper (qubits) to Bob, that CAN be intercepted and manpulated by Eve.

Steps:

1. Alice sends a bunch of magic paper to Bob.

1.5 Eve potentially intercepts the shipment and manipulates it.

2. For every piece of paper, Alice randomly decides which digit to check. Bob does the same independently.

3. Alice and Bob tell each other over the classic channel, that Eve cannot intercept, which digits they checked.

4. They discard the papers where they checked different digits, and use the rest to form a One Time Pad.

Still implies FTL?

In the global race for valid metaphors for quantum theory, I thought this was a pretty good one, thank you.

As another user pointed out though, it's not quite that simple. After reading up some more, I think this is a better analogy:

You have 2 magic entangled coins. Each coin has a heads and a tails side.

If you both look at heads first, entanglement guarantees they will show the same US president. If you both look at tails first, entanglement guarantees they will show the same US building. However, and this is where it gets weird, if your friend looks at tails first, and you look at heads first, then your respective coin presidents and buildings will be random.

As you can see, this does not allow you to communicate with your friend faster than light. However, if you send a message to your friend using entangled coins, he can check if an eavesdropper intercepted your message by first looking to see that every coin has the same president on it. If some coins have a different president, it means that an eavesdropper intercepted your coins and looked at tails first somewhere along the way. This relies on you and you friend agreeing ahead of time that you should always look at heads first.