Researchers Advance 'Quantum Teleportation'
jpl.nasa.gov
jpl.nasa.gov
NO NO NO! Ten thousand times no! Bob's photon does NOT change state as a result of Alice's measurement. It is in exactly the same state that it was in before: entangled, which is to say, if you consider it in isolation, it is in a quantum mixed state. NOTHING changes on Bob's side as a result of Alice's measurement.
It's bad enough that the popular press chronically gets this wrong, but NASA really ought to know better.
As usual in these situations, it depends on being precise about what one is referring to with words like "state". But with the common definition -- a density matrix updated to incorporate all macroscopic data -- the state of A certainly does change following the measurement of B. It goes from fully mixed to pure.
Of course, Bob's personal epistemic state (which doesn't include data that he hasn't yet received from Alive) doesn't change.
You can try to say that Alice and Bob's photons have merely become entangled with the measuring apparatus, or some similar many-worlds-type statement, but then you'd be using "state" in a very different way than the vast majority of experimental physicists. You might think that definition better fitting with reality, but it certainly wouldn't make the NASA press release wrong.
The difference between a mixed and a pure state is simply a difference in mathematical perspective, not a difference in the underlying physical reality.
> There is no experiment Bob can perform on his photon that will reveal to him whether or not Alice has measured her photon or not (note that this remains true EVEN AFTER he has received Alice's bits).
I'm not sure what you mean here, but a reasonable interpretation of your words would be false. You consider a situation where Bob has received bits from Alice even when she might not have actually made a measurement. If so then I guess you're saying that Alice just makes these up? If so, then Bob can certainly check to see if Alice has actually made the measurement she claims to have by making a local measurement on his photon, and this can result in an outcome that lets Bob definitively determine that Alice is lying to him. [Of course, sometimes Bob's result agrees with Alice's claimed bits; in this case, Alice has simply guessed correctly for what she will end up receiving in her (now fully determined) experiment.]
I have met many people for whom this is their day job who nonetheless don't understand this.
> Bob can certainly check to see if Alice has actually made the measurement she claims to have by making a local measurement on his photon
No, he can't. The best he can do is determine (probabilistically) that the bits Alice gave him are not the result of such a measurement. But he cannot know whether or not Alice's measurement was actually performed.
In other words, Bob cannot distinguish:
1. Alice does not perform a measurement, but rather simply pulls two bits out of a hat.
2. Alice does perform the measurement, but sends Bob two bits pulled out of a hat rather than the results of her measurement.
He cannot make this determination EVEN PROBABILISTICALLY, i.e. after aggregating many trials all prepared the same way. Because of this, it is wrong to say that Alice's measurement changed the state of Bob's photon.
Of course, Bob can distinguish between Alice sending him bits pulled out of a hat and bits resulting from her measurement, in which case he can know that Alice must have performed the measurement. But that's a red herring.
The misunderstanding you're now addressing arose because it doesn't make sense for you to say "this remains true EVEN AFTER he has received Alice's bits" if you're describing a situation where Alice is always making up the data. (Why would Bob ever look at it if it's always made up? It has nothing to do with the rest of the problem.)
With your clarification, I know understand what you mean by determining "whether or not Alice has measured her photon or not... EVEN AFTER he has received Alice's bits". But this doesn't change my previous comments on the common definition of "state".
That's certainly possible, but I wouldn't take it as a foregone conclusion. Nonetheless, I apologize if I came across as strident.
> Why would Bob ever look at it if it's always made up?
Why would he not? He doesn't know whether or not the bits are made up. Let's call them "corrupted" because it doesn't have to be intentional duplicity on Alice's part. It could be simple experimental error, or a noisy communications channel, or a MITM attack. None of these are distinguishable by Bob from Alice having not made a measurement. In any event, Bob might look because he wants to determine if the bits are corrupted. Or he might look because he thinks he's participating in the quantum teleportation protocol, notwithstanding that he's actually not because the bits are corrupted. Note that for any given bit pair he has to choose one or the other: teleport, or check for corruption. He can't do both.
It is also worth noting that even the possibility of corruption is enough to debunk the idea that Alice's measurement results in a physical change on Bob's side. Bob can tell (probabilistically) that there is corruption happening, and he can put a probabilistic upper bound on the amount of corruption that is happening, but under no circumstances can he tell which measurements are corrupted and which are not. One in four corrupted measurements will appear to be genuine by pure chance, and there's no way for Bob to know, even probabilistically, which is which.
After a few curses of quantum mechanics (with the Sakurai book) and working in the field I still not sure if the press release is misleading or just wrong.
One of the important details is that Bob can't do any experiment to distinguish the photon before Alice measurement and the state of the photon after Alice measurement. If it's not possible for him to distinguish the states, has it really changed?
On the other hand, if Bobs makes a measurement after Alice measurement, the result should "agree" with the result Alice measurements. So, has something changed?
I think that the press release it's completely misleading and perhaps wrong.
There is absolutely no doubt that if the reader applies an intuitive classical interpretation of the term "state" to what physicists mean by a quantum state, then the reader will end up with some wrong impressions (and some right ones). The fact is that there are certain things that are going on that just don't map well on to normal, classical language. And this is not the readers fault; he's a normal, lay human being, and really smart people have been fighting over how to interpret the (unambiguous) experimental data for almost a century now without reaching a consensus.
Now, it would probably be better if physicists used the term "qustate" to refer to the state, and that they used this press releases, and that they said stuff like "when Alice makes her measurement, the qustate of Bob changes instantaneously". That way no one would go applying their classical intuition about what a "state" ought to be to the density matrix. Instead, they would ask "what's a 'qustate'?", and someone would say "well, it's sort of like a classical state...but it's not the same...and it's sorta like an epistemic probability distribution...but also not really...and the difference are subtle and very profound and you have to be careful and it takes a good amount of studying before you can understand." And that would be great and maybe a few more people would go actually read about it. But as it stands physicists are more than happy to allow laymen to misinterpret their terminology when it leads to their work sounding more exciting and getting more funding. There is definitely something of a Motte-and-Bailey going on. ( http://slatestarcodex.com/2014/11/03/all-in-all-another-bric... )
> On the other hand, if Bobs makes a measurement after Alice measurement, the result should "agree" with the result Alice measurements. So, has something changed?
Actually, the mere agreement of Alice and Bob's measurement doesn't really give evidence that anything on Bob's side has changed. If I jumble a blue marble and a red marble in an urn and then put them in separate brown bags and give you one at random, then when you look in your bag that will instantly determine what I'll get when I look in mine, but it didn't change anything about my bag in the normal, physical sense.
The way in which quantum mechanics differs from this situation is subtle but significant.
Yes, I think you hit the nail on the head here.
The two entangled photons were once close to each other, just like the two sides of the coin. So what's the difference here?
Looking at a photon you can't tell whether someone else has looked at the entangled photon. Same with the sides of the coin.
http://www.scientificamerican.com/article/quantum-entangleme...
We can see this by considering two electrons in an entangled spin state - say, one is spin up, and the other is spin down, but the entangled state means you don't know which is which, only that Alice and Bob will get consistent answers when they measure the spin in the vertical direction. At this point, everything maps fine to the two-half-coins idea, all we know is that they have opposite spins.
What's different in the quantum case is that Alice and Bob could instead decide to measure the spin in the left/right direction. Following the rules of quantum mechanics, a given spin up or down state has an undetermined spin left/right state, so when you measure the spin in the left/right direction it has exactly 50% chance of being each one.
If the original states were really just like the coin halves, this new measurement would be simply uncorrelated between Alice and Bob - they'd start with different states (up or down), but the left/right measurement would destroy that information and they'd both get a random answer because the individual elecrons end up with an individually random left/right spin direction.
The reality is actually different; if we do the measurement maths on the quantum state rather than assuming it's predetermined like the coins, it turns out the left/right spin is still entangled. That means that when Alice and Bob measure the spin in the left/right direction, they'll always find that one of them gets left and the other gets right. This would not be possible if the quantum states were predetermined like the coins.
So, the coins analogy is not a bad way to understand some of the basics of what you expect, but it absolutely is not a fully accurate description of what's going on. Maybe you already knew that, but I wanted to be clear that there's very much more to entanglement, because this is the source of several common misconceptions.
(Of course quantum teleportation is a further thing again, but the extra non-classical mathematics of entanglement are still important, it's not just coin halves.)
Suppose Alice and Bob had unlimited pairs of marbles labeled "RU" "RD", "LU" and "LD" paired up with their opposites respectively, e.g. RU with LD. Alice would randomly select four marbles, one from each pair, and Bob would select the corresponding opposites. Now they separate and go to their homes, not knowing what the marbles are.
Alice checks the first letter on the marbles only, and sees that she has R* and R*. She concludes that her spin is "LEFT" and that bob has the "RIGHT" marbles. Now, she decides to check all the letters on her marbles and realizes she has, say, two RT marbles. She knows that Bob has two LD marbles.
Can a spin be not 1 or -1? Could it be in between? That would be the case here if Alice had RU and RD, and once she checks both letters, she knows what Bob has as a result.
But in the classical case discovering first letter doesn't give you any information about the other. Doesn't that capture everything?
> Why would the measurement of Up/Down spin destroy information about Left-Right spin in the classical case?
It wouldn't, if you like, which would make it another thing that would be different in classical mechanics, though it's a little strained because it's assuming a lot about quantum states being like classical states.
In quantum mechanics the different spin operators do not commute, which means if you measure it in the vertical direction (and get e.g. up) then in the left-right direction, you get each of left or right with 50% probability. But then if you measure it in the up/down direction you don't get up again, you get up/down each with 50% probability, the original state is irrelevant. This is obviously different to your marbles, which just have letters that don't change.
> Can a spin be not 1 or -1? Could it be in between?
No. When you measure the quantum state you get an eigenfunction, though the state before collapse could be a superposition. Indeed, this is the case for different directions - spin up is a superposition of equal parts spin left and spin right in the horizontal spin basis, which is why you get each direction equally if you measure it in that direction.
> Doesn't that capture everything?
You're still trying to encode everything in a hidden variables theory, where the quantum states secretly know everything beforehand about what it will do, but the observer can't access the information without performing specific measurements. This immediately fails as above, because the quantum states inherently don't have fixed up/down and left/right components and each measurement in a different basis gives a random result.
You can try to fix things by adding more complex rules about the letters on the marbles changing when you read them, but it turns out there are fundamental limitations on what physical results any such theory can predict. This is famously addressed by Bell's theorem (as in, seriously famously, this is really important), which demonstrates specific limitations on what physical results are allowed by such models, and experiments have shown that quanum mechanics does breach these limitations. I'm not sure how to explain more simply what's going on though.
(Strictly, we can allow hidden variables (though more complex than a predetermined left/right and up/down as above) by breaking the speed of light to let the separated states communicate instantly, but this brings up its own problems.)
Sheesh, these are awfully handwavy questions for someone who was in a math ph D program. I should really sit sown and learn quantum mechanics for a while with the math. How long do you think it would take to reason intelligently about it? Going by what Feynman said, maybe I can't.
Bell's theorem remains true, but pilot wave theory achieves the quantum results by sacrificing locality instead of hidden variables.
> how does the description of entanglement as "spooky action at a distance" not violate those?
It's just a name, and an old one at that. I suppose if you ascribe it to non-locality then it really does involve something FTL on some level, but even with a standard locality-preserving, no hidden variables theory, no information travels faster than light so you don't actually hit a FTL problem. The strange thing is that the quantum state appears to behave consistently regardless of its spatial extent, which is weird.
> How long do you think it would take to reason intelligently about it?
I would have thought that someone in a PhD mathematics program would be well equipped to understand the mathematics - maybe the hard part is finding a good resource that takes things in a good order. I'm afraid I can't really recommend anything, though Feynman's stuff is probably good.