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Understanding Quantum Entanglement - with Philip Ball

Apr 09, 2020
I recently gave a talk here in RI on

quantum

mechanics and was very happy to see it got a great response; However, some people, some viewers of that talk, expressed some bewilderment or worse about an analogy that I used during it, so I wanted to be here to discuss that analogy in a little more detail, hopefully a little more clearly and explain what it is really about, what you are really trying to show, is an analogy to try to understand the

quantum

phenomenon called

entanglement

and, first of all, I want to point out that the analogy is not mine, it is not something that there invented, is adapted from an analogy that was devised in the late 1990s by two physicists Sandu Popescu and Daniel Rollick and they were trying to understand the implications of this quantum property of

entanglement

and self.
understanding quantum entanglement   with philip ball
We'll come back at the end to what you were exploring now. I think some people got the impression that this was just a very complicated way of talking about entanglement. Not that this analogy is actually doing anything a little more than that, but First I'll talk about what entanglement is, it's what happens when two quantum particles interact. It has to happen and what results from that is that those particles, once they have interacted, become entangled and that means that their quantum states are interdependent. There is a correlation between them, so that if one is in a particular state, the other has to have some other particular state depending on the type of entanglement they have, so the classical example would involve, say, two electrons and the electrons have a quantum property. called spin, which you don't need to know anything about other than the spin of an electron can have two values, it's a bit like a kind of quantum heads or tails, the electron can spin up or down and if the electrons become entangled then this you can create a situation where those two spins are correlated so that if one of the electrons has an up spin, then the other must have a down spin.
understanding quantum entanglement   with philip ball

More Interesting Facts About,

understanding quantum entanglement with philip ball...

This is a prediction of quantum mechanics and it was pointed out that this property is so. The entanglement phenomenon can occur, it was pointed out by Albert Einstein in 1935 and he thought there was something wrong with it. I explained in the talk how we can think about entanglement in some ways, this correlation between the two states of the electrons in some ways is a bit like having two gloves, one for left-handed and one for right-handed, now if you imagine that you have those two gloves and you send them to two people in different signs of the world, perhaps and these two people were going to find them.
understanding quantum entanglement   with philip ball
Shortly, I again called Alice and Bob and they know that these gloves are a pair, so as soon as Alice receives her glove, opens the package and discovers that she has the glove for her left hand, she knows immediately that Bob must have the right. glove because there is a correlation between them there is nothing magical about how you get that information it is just simple logic however here is the complication in quantum mechanics because niels bohr the danish physicist who pioneered early quantum mechanics suggested that in the case of quantum particles is not the fact that they have this property, whatever the spin or whatever, all the time they just have that property with a fixed value when we observe it, so for these two entangled photons, if we think about sending them to to Alice and Bob Bohr, he said as they go out, they don't have a fixed orientation of their spin, all we can say is that those spins are correlated, so if Alice measures her electron and finds that it has an up spin, then Bob's will have a downward spin, but that spin was not determined until Alice measured it and this is where Einstein felt there was a problem with entanglement because it seemed to indicate that Alice's act of measuring the spin of her electron it somehow affected Bob's spin, so Alice had figured out that the spin had to be increased somehow.
understanding quantum entanglement   with philip ball
Magically or spookily, as Einstein said, that seemed to transmit some kind of influence to Bob's spin to make sure he had a downward spin. Alice could also have measured her electron and discovered that it had a downward spin, in which case Bob's would have spun up, so there seemed to be what Einstein called a spooky action at a distance implicit in Bohr's idea about quantum mechanics. Einstein and two colleagues, Podolsky and Rosen, suggested in 1935 that there actually has to be some alternative to this because spooky action at a distance shouldn't. In physics Einstein had shown that it is impossible for any signal or information to be transmitted faster than light and therefore you cannot have this instantaneous action at a distance, there has to be some time for a signal to spam the distance and then Einstein suggested that what must be happening is that from the beginning these two electrons had some property that somehow already fixed their spins, it's just that it was a property that we couldn't measure.
He called them hidden variables, so they couldn't be found. in any experiment which of the two possible spins Alice's electron had when it was heading towards her, but it was nevertheless fixed and that then reduces the situation to being like the left hand in the glove of the right hand, which were right-handed left-handers. They were delivered all the time in transit, so there were these two possibilities of what was the intertwining between Bohr's vision and Einstein's. The problem was that there was no obvious way to distinguish between them because they both predicted the same outcome, which was that we would measure either Alice or Bob.
He would measure that there are these correlations that exist between the spins of these two entangled electrons. How do we know if that is due to hidden variables or something else? Bohr was suggesting that change in 1964 when the Irish physicist John Bell suggested an experiment was in that case at that stage it was just a thought experiment that he said would allow us to distinguish between these two possibilities and it is John Bells experiment that these boxes, these quantum boxes are imitating personally. I've never seen an explanation from John. The bell experiment is easy to follow, so instead of trying to explain John Bell's experiment, that's what these boxes are for, that's how this box analogy works, there are two boxes, they're slot machines in which you can put a coin in and Take out a toy so you can put it in, they will take one pound or two pound coins and one of two types of toy will come out, either a rabbit or a dog, and there are particular rules for each type of machine so that if you put that it will tell you if you put a certain point then you will get a certain animal okay and we have to find combinations of which coins give what type of animals to satisfy three rules.
I'm just going to postulate these rules but, of course, they have actually been carefully chosen to replicate the kind of situation that quantum mechanics imposes in John Bell's experiment and the rules are as follows: The first rule is very simple: if Alice You put 1 pound coin in your box, it will spit out a rabbit. The second rule is that if both Bob and Alice put £2 coins in their boxes, then the boxes will produce a rabbit and a dog and it doesn't matter which direction. will have that combination, the third rule is that any other combination of coins instead of two pound coins will produce two rabbits or two dogs, so we have to find inputs and outputs that satisfy these three rules, so what can they be? ?
Work with them, we already know what the result of Alice's box should be, if she puts in a pound coin, it has to be a rabbit, that's the first rule. Now when we think about it, this means that it doesn't matter what currency, whether it's a pound. or two pounds that Bob puts in his box, he also has to produce a rabbit, because if Alice has produced a rabbit with one pound, then the only way we can get a dog is that if they both put two pounds, Alice already put one . pound, so Bob's box has to produce a rabbit in either case with one pound or two pounds, so we've almost figured out what our rules should be, so all we have to figure out now is what a pound two pounds.
The coin in Alice's box will produce well, think about it if she puts in two pounds. Bob puts two pounds two. We also have the second rule which says that two two pound coins have to produce a rabbit and a dog, so that must mean that two pounds in Alice's box produce a dog and then we satisfy the second rule. The problem with that is that those exits, entrances and exits violate the rules otherwise because for one pound two pounds we have this combination. of the rabbit and the dog, but we should only get that if they both weigh two pounds, so one of the four possible permutations violates the rules and no matter how you try and do this, no matter how you try and think of different combinations, you will find that you will never be able to do better than three out of four times.
If he believes that he has found a solution that satisfies these three rules all the time, in all four cases it is likely that he has found a solution. a solution like this a solution in which let's say that Alice's box alters its output depending on the coin that Bob put in. There is no physical way if these boxes are not connected. There is nothing that happens between them. There is no physical form in which we can build. A machine that does that somehow magically or telepathically knows what the other person has put in its box, so that's not going to work, however, there is a way that we can allow that to happen, which is that Let's make a physical connection. between the boxes that sends a signal between them so that Alice, so that Bob's box, for example, would receive a signal telling it what Alice has put in its box and could then alter its output accordingly, is perfectly possible produce a mechanism like that, the problem with that is, Bob has to wait until the signal is received from Alice's box, so until she puts in her coin and the signal has been sent, he has to wait until that happen before you put your coin in so your cashier knows what to do.
That takes a finite amount of time, even if the signal travels at the speed of light it will still take some time to get there, so it won't work if we try to make boxes that satisfy these rules instantaneously when Bob and Alice put their coins exactly in the same moment we want an instant solution to this problem, so that will never happen, at least it will never happen with classical boxes, if they are quantum boxes, if we allow them this property of quantum entanglement, so that the two boxes can be its inputs and outputs can be correlated in some way then we can do better and in fact we know exactly how much better we can do because the laws of quantum mechanics the rules the mathematical equations allow us to calculate exactly how much more often we can satisfy the four rules compared to the classical case or in the classical case we can only get it three out of four 75% success rate quantum mechanics tells you that you can get about 85% success rate and white white 85 well it's just a number that the equations give you, it's actually more precisely, more precisely, it's a number that involves a square root of 2, we don't have to worry about it because it's only about 85%, but I'll get back to it.
Let's come back to why 85% later, so quantum mechanics allows you to do better if these two boxes are entangled and this is really what the Bells experiment allowed you to do. You did the equivalent measurement with two particles that were entangled and Bob and Alice were doing it. measurements by making decisions about how to make those measurements and seeing how strong the correlation was between them according to classical physics, you could only get a 75% correlation, but the same was true. John Bell showed that Einstein's hidden variables were only if quantum mechanics went further. that, as Bohr suggested, you could do it better and get 85% success, as I say, this was just a thought experiment by John Bell, but very soon physicists realized that you could really do it: you could create two entangled particles and make measurements. and this was done, it was done first in the 1970s and then more definitively in the 1980s and since then it has been done many, many times, in many different ways, each time the result has been very clear : the classical limit or the limit of hidden variables of You always exceed 75% correlation between particles, you get this 85% success, so this suggests that Einstein's idea that there are things called hidden variables that fix the properties of quantum particles before measuring them, this does not apply, it seems that Bohr was at this time, this does not imply, as sometimes you can hear that there really is some spooky action at a distance.
Many times, when experiments like this have been performed, their newspaper headlines have proclaimed that Einstein has been proven wrong and that the action is spooky at a distance. This is some really creepy action at a distance, that was Stein's interpretation of the entanglement involved, but it's actually a better way to think about thetangle to say something a little different and one way to think about it is to say that once the two boxes become intertwined, they are no longer separate objects, so what happens here is completely the result of what happens here. In some quantum sense, they are the same object and that remains the case no matter how far apart they are; even if the particles being measured were separated were on opposite sides of a galaxy, in some sense they are still a single quantum entity.
Another way to think about it is to say that there is some kind of information exchange between them and this is really what Popescu and the Rolex quantum boxes do. It was about expressing this situation in terms of a kind of information exchange, physicists call this quantum nonlocality and it's distinct from this notion that somehow making a measurement on this particle is transmitting information, is transmitting a signal to the other particle to fix what the value of its property is that it doesn't. If it happened, it would violate special relativity as Einstein suggested, but quantum mechanics tells you something else: there is a property called quantum nonlocality, which is very difficult to find words for, but is a real property of the world.
If you see headlines saying that spooky action from a distance is real, don't believe them now. I want to finally go back to what popescu and ralick were trying to do with their boxes because one of the physicists is more disgusting, Aronoff, than maybe what we're seeing here. This quantum nonlocality is a kind of extension of the normal laws of cause and effect as far as special relativity allows, so that in some ways quantum mechanics almost violates the spirit of special relativity without actually violating it in practice, without allow it to transmit information faster than light, maybe quantum mechanics is doing this, you know to the limit of what is physically possible, well, Popescu and Rowlett thought, let's look at that, can we imagine a case where there is some kind of entanglement that works better than Quantum mechanics that works better than 85% and they thought about it and came up with the idea that these two boxes that they showed could have a set of rules that, without violating special relativity, allows you a correlation of the One hundred percent, you are not physically breaking any laws.
Let's say we know we have a situation like this, if you like some kind of super quantum correlation, then the question is why isn't the world like that? We often think of quantum mechanics as something added. or something different from classical mechanics that classical mechanics has this kind of 75% success rate, in this case quantum mechanics does something else, so we think you know where that comes from, why quantum mechanics allows you to do these things that I can't do the classic. Popescu and Radek approached it from another angle because they showed that actually things can be even if you like them more quantum than they are, and then why aren't they?
And that raises a new question if we could understand why quantum. Mechanics is limited in what quantum nonlocality can make limited to this 85% figure instead of 100%. If we could understand that, then maybe we would understand a little more about why the world has these quantum properties that it seems to have at the moment. fundamental particle level, if you still find this analogy a little confusing then probably what you need to do is look it up in my book Beyond the Strange, which talks about this and more and goes into more detail about what quantum entanglement does and does. .
I don't want to say and also about how we are starting to use it in quantum technologies like quantum computing and quantum cryptography and let me remind you that if you haven't subscribed to the RI YouTube channel yet, then you should.

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