While I understand that Alice can’t send Bob a specific digital message because forcing a particle’s spin state would distentangle the particles, what if the outcome of a coin flip was sufficient information? Let’s say General Bob and General Alice were going to cooperatively invade Planet X and they were neutral as to who invaded the South pole of the planet and who invaded the North Pole but wanted to keep the information from Planet X so it wouldn’t be able to create a counter to each General’s strengths (yes I’ve made this unnecessarily complicated but now I’m committed). They are told to check the spin state of their entangled particles at a certain time and whoever had a down-spin invaded the South and vice versa. Since I know information, at least as defined by physicists in this context, can’t travel faster than light, either I’m misunderstanding how entanglement works or physicists are using a qualified definition of information. Which is it? Thanks in advance.
I’ve come up with the same scenario when thinking about useful applications of this. I don’t remember what the downside was myself.
Looks like Planet X is fucked. 
What information is being passed faster than the speed of light in this scenario?
What’s the difference between this scenario, and one where Alice and Bob take the Ace of Spades and the Queen of Hearts, put a card into two sealed envelopes, and on D-Day they open the sealed envelopes. If Alice sees the Ace of Spades, she knows instantly that Bob has the Queen of Hearts, if she sees the Queen of Hearts, she knows instantly that Bob has the Ace of Spades.
No superluminal transfer of information has occurred in this scenario of sealed envelopes, right?
The only difference here is that the entangled particles haven’t decided which state they are in until Alice looks, while the cards have. But it’s the exact same amount of information.
Well like you said, in the case of the entangled particles, the information hasn’t been “created” yet so there is no information to transmit. In the case of the playing cards, the information as to who will be invading where already existed and traveled, in some form, subluminally. I think your point is touching on where I’m wrong, I just don’t quite see the whole picture.
Indeed, you can effect, for example, teleportation of a quantum state after transmitting classical bits of information, but not without doing so.
Measurements on entangled particles can be correlated; that’s kind of the point. No information is transmitted, though, and the result of each measurement (disregarding the other one) is random, as expected.
Yes, the generals can coordinate their attacks in this way, and no, it doesn’t violate any rules, and no, it doesn’t even need quantum mechanics to get this effect.
But, as noted, it’s not transferring any information.
Maybe the missing point for some people is that a pair of entangled particles can only be created when the particles are in the same spot. Then, couriers would need to put the particles in separate boxes and carry the respective boxes to Alice and Bob. If they’ve got couriers who can do that, then the couriers could have just measured the spin before they left (or flipped a coin or whatever other random event they want) and used the result to put the Ace and Queen in one or the other box and brought that to the respective Generals.
Well, that’s the explanation I finally understand. And it’s so obvious and easy, when you think about it.
As I guessed, my problem is either with my understanding of the definition of information or transmission as it’s used in this context. From a colloquial sense, it seems like information is being transmitted FTL because Bob is doing something that answers the question “Where should I invade?” for Alice nearly instantaneously. Why isn’t the result of a coin flip information?
I do see your point. But there is a difference though in the sense that the couriers’ information would be different than if Bob had measured it at Place Y, Time X. It would be a different coin flip. While the particles are entangled, there is no coin flip result. The information about who is invading whom simply doesn’t exist. I see your point but do you see mine? I know I’m wrong, I guess I’m looking for how information is specifically defined in this context.
You’re not wrong about the result that entangled particles can generate, and the fact that it could it could be strategically useful. You could randomly pick which general attacks which target just before the attack begins, so that the defenders cannot possibly plan ahead; yet ensure that one general attacks south and one attacks north. It’s notable, however, that you cannot use this technique to set up a scenario where both generals attack the same target, even if the target is chosen randomly.
And you’re also not wrong that the two particles must be able to communicate certain information between one another instantaneously at arbitrary distance. That’s the “spooky action at a distance” that is so difficult to make intuitive sense of in QM. And observers can passively read the correlated states of the two particles instantaneously.
What cannot happen is for one observer to actively pass information to another distant observer; observers cannot “choose” what information is exchanged instantaneously between the particles. There is no way for one general to tell the other general “attack south”. What you’re trying to pin down is the No-Communication Theorem.
Maybe I’m missing something. If you could send the binary outcome of a coin flip, why couldn’t you send multiple binary outcomes to form a digital message?
Maybe it’s more like a coin toss where a third party (who is deaf, dumb, and blind) does the toss and has no way of communicating with A and B. So A and B could see the coin toss and see the result at any given moment, but with no way of inputting a pattern themselves. Honestly, it seems like no better than having synchronized watches and both being able to read the time simultaneously, even a light-year apart. Yes, you know what the other guy or gal’s watch says because they’re synchronized, but you can’t then move the minute hand back on yours and expect the other’s to do the same.
How would you do that, when you have no control over the random outcomes of the coin flips?
Oops, on rereading this sentence is completely wrong, obviously you could get them to attack the same target if it’s chosen randomly and you don’t care which.
How does it not require QM, if a requirement is that the coordinated action be chosen truly at random at the last moment before the attack - i.e. the information cannot be intercepted by the enemy ahead of time, even in principle? This is equivalent to saying “no hidden variables”.
In the scenario as given, it indeed doesn’t require QM—the same sort of behavior could be obtained by local hidden variables, i. e. each box containing a particle with a definite, but up until measurement simply unknown, spin value. That is, you could replace the scenario with one in which the information about which pole to attack is sent from the source of both entangled particles to their eventual measurement, and there’d be no way to know the difference.
In particular, if the enemy intercepted the particles, and measured them, they’d know which pole would be attacked beforehand, and a re-measurement in the same basis of both generals at the point of attack would tell them the same information. In this sense, no information is being transferred between the generals at the moment of measurement.
A crucial part of this setup is that it has to be decided beforehand in which basis a measurement must be undertaken, as both generals must measure in the same basis (e. g. spin in X-direction vs. Y- or Z-direction) in order to observe appropriately (anti-)correlated outcomes. If an enemy interceptor then were to measure in the wrong basis, both generals would no longer be guaranteed to attack opposing poles, but of course, there’d be no way for them to know that before getting together and comparing notes, so also in this case, they could not detect enemy meddling.
There would be a way to be certain that nobody intercepted each particle, and hence, to ensure that the information is ‘created’ only at the point of measurement, but in order to do so, they’d have to meet and compare notes at some point. Essentially, the idea is that you use a sufficiently large number of entangled particle pairs, and using some (random) part to verify the violation of a Bell inequality (which would not be verified if an enemy had interfered). Essentially, this is the so-called Ekert protocol for quantum cryptography.
However, in order to do so, both generals need to exchange information about their measurement results, and the bases they used; at which point, of course, you don’t have any FTL information transfer anymore.
So the reason there’s no FTL information transfer in the original case is that there’s no way to experimentally verify whether there’s actually an entangled particle pair distributed between both generals and still coordinate the attack without further communication. If both generals just measure the particles and attack, then they may just reveal information contained in the particles from the source; and if they were to verify that the particles are not secretly in some definite, non-entangled state (i. e. the information is actually not in there before measurement), they must communicate. So each case is in fact consistent with information transfer only ever happening with less than light speed.
Now, of course, it may be that information is transferred FTL, and nature just conspires against us such that we can never actually verify that fact—indeed, that’s sorta what happens in Bohmian mechanics. But a difference you can’t observe doesn’t really make a difference (and hence, fails to be information ;)).
By the way, it also wouldn’t work to coordinate the attack using many pairs of particles, and meeting up later to see whether a Bell inequality had been violated: to coordinate, both parties need to know what basis the other measures in, but to violate a Bell inequality, they need to randomly measure different bases at random; if they agree on a recipe to measure in different bases, then we can again use a local hidden variable theory to explain the observed violation, and have no FTL information transfer.
I think I get it. So would it be accurate to say that both parties can see that there is a coin flipping at random, but as soon as they try to specifically set the coin to heads or tails, it goes away?