# Understanding Quantum Entanglement - with Philip Ball

I recently gave a talk here at the RI on

### quantum

mechanics which I was very pleased to see got a big response however some people some viewers of that talk expressed some bafflement or worse about an analogy that I used during it and so I wanted here to go through that analogy in a little more detail hopefully a little more clearly and explain what it's really about what it's really trying to show it's an analogy to try to understand the### quantum

phenomenon called#### entanglement

and I want first of all to to point out that the analogy isn't mine it's not something that I've invented it's 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 I'll come back at the end to what it was that they were exploring now I think some people had the impression that this was just a very complicated way of talking about#### entanglement

it's not doing that this analogy is actually doing something a little more than that but I'll talk first of all about what#### entanglement

is it's what happens when any two### quantum

particles interact it has to happen and what results from that is that those particles once they've interacted they are entangled and it means that their### quantum

states are interdependent there's a correlation between them so that if one is in one particular state then the other one has to...have some other particular state depending on the kind of

#### entanglement

that they have so the classic 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 that the spin of an electron can have two values it's a bit like a sort of### quantum

heads or tails the electron can be spin up or spin down and if the electrons become entangled then this may create a situation where those two spins are correlated such that if one of the electrons has a spin up then the other one must have a spin down now this is a prediction of### quantum

mechanics and it was pointed out that this property this this phenomenon of#### entanglement

can happen it was pointed out by Albert Einstein in 1935 and he figured that there was something wrong about it I explained in the talk how we can think about#### entanglement

in some ways this correlation between the two states of electrons in some ways it's a bit like having two gloves a left-handed and a right-handed glove now if you imagine that you have those two gloves and you send them out to two people in different signs of the world maybe and these two people were going to meet them again shortly a called Alice and Bob and they know that these gloves are a pair and so as soon as Alice receives her glove and opens the package and finds she has the left-handed glove then she knows right away that Bob must have the right-handed glove because there is this...correlation between them there's nothing magical about how she gets that information it's just simple logic however here's the complication in

### quantum

mechanics because niels bohr the danish physicist who pioneered early### quantum

mechanics suggested that in the case of### quantum

particles it's not the fact that they have this property whatever it is spin or whatever all the time they only have that property with a fixed value when we observe it so for these two entangled photons if we think of sending those out to Alice and Bob Bohr said while they're going outwards they don't have a fixed orientation of their spin all we can say is that those spins are correlated so if Alice then measures her electron and finds it has spin up then Bob's will have spin down but that spin wasn't determined until Alice measured it and this is where Einstein felt there was a problem with#### entanglement

because it seemed to indicate that the act of Alice measuring her electron spin somehow affected Bob spin so that one Alice had found the the spin had to be spin up somehow magically or spookily as Einstein said that seemed to sort of transmit some kind of influence to Bob spin to make sure that it was spin down Alice could equally have measured her electron and found that it had spin down which case Bob's would be spin up so there seemed to be this what einstein called a spooky action at a distance implied by Bohr's idea of### quantum

mechanics Einstein and two...colleagues Podolsky and Rosen suggested in 1935 that actually that there has to be some alternative to this because spooky action at a distance shouldn't be allowed in physics Einstein had showed that it is impossible for any signal any information to be transmitted faster than light and so you can't have this instantaneous action at a distance there has to be some time for a signal to to spam the distance and so Einstein suggested that what must be going on instead is that all along these two electrons had some property that somehow fixed their spins already it's just that it was a property that we couldn't measure he called them hidden variables so you couldn't find out in any experiment which of the two possible spins Alice's electron had as it was going towards her but nevertheless it was fixed and so that then reduces the situation to being like the left handed on the right-handed glove which were left-handed right-handed all along in transit so there were these two possibilities for what

#### entanglement

was about Bohr's view and Einsteins view the trouble was there was no obvious way of distinguishing between them because they both predicted the same outcome which was that we would measure or Alice and Bob would measure that there are these correlations that exists between the spins of these two entangled electrons how do we know if that's due to hidden variables or due to something else that that that Bohr was suggesting that change in 1964...when the Irish physicist John Bell suggested an experiment it 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's John bells experiment that these boxes these

### quantum

boxes are mimicking personally I've never seen an explanation of John bells experiment that is at all easy to follow so instead of trying to explain John bells experiment that's what these boxes are for so here's how this box analogy works there are these two boxes they're machines slot machines into which you can put a coin and get out a toy so you can put in either they will take either one-pound coins or two pound coins and out will come one of two types of toy either a rabbit or a dog and there are particular rules for each kind of machine so that if you put in that will tell you if you put in a certain point then you will get out a certain animal okay and we have to figure out combinations of which coins give which kind of animals in order to satisfy three rules I'm just going to postulate these rules but of course they've actually been carefully chosen so that they replicate the kind of situation that### quantum

mechanics imposes in John bells experiment and the rules go as follow the first rule is very simple that if Alice puts in a 1 pound coin into her box it will spit out a rabbit the second rule is that if both Bob and Alice put in 2 pound coins into their boxes then the boxes will...produce one rabbit and one dog and it doesn't matter which way round that is that they will have that that combination the third rule is that any other combination of coins rather than to two pound coins will produce either two rabbits or two dogs so we have to find inputs and outputs that satisfy these three rules so what can they be well let's work through them we know already what the output of Alice's box has to be if she puts in a one pound coin it has to be a rabbit that's the first rule now when we think about it this means that no matter which coin whether a one pound or two pound Bob puts into his box it has to produce also a rabbit that's 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 in two pounds so Alice already put in one pound so Bob's box has to put has to produce a rabbit in both of those cases with one pound or two pound so we've almost already figured out what our rules have to be so all we need to figure out now is what a two pound coin in alice's box will produce well let's think about it if she puts in a two pound Bob puts into two pound two we've also got the second rule which says that two two pound coins have to produce a rabbit and the dog so that must mean that a two pound in Alice's box produces a dog and then we satisfied the second rule the trouble with that is that those outputs inputs and outputs violate the rules in another case...

because for a one pound at a two pound we've got this combination of rabbit and the dog but we're only meant to get that if they both put in two pounds so in one time out of the four possible permutations the rules are violated and no matter how you try and do this no matter how you try and think of different combinations you will find that you can never do better than three times out of four now if you think that you have found a solution that satisfies these three rules all the time in all four cases it's probable that you've come up with a solution like this one a solution in which let's say Alice's box alters its output depending on which coin Bob put in there is no physical way if these boxes are unconnected there is nothing that passes between them there is no physical way in which we can build a machine that does that as somehow magically or telepathically knows what the other person has put in into their box so that's not going to work however there is a way that we can that we can allow that to happen which is that we produce a physical connection between the boxes that sends a signal between them so that Alice so that Bob's box for example receives a signal telling it what alice has put into her box and then it might alter its output accordingly it's perfectly possible to produce a mechanism like that the trouble with that is that bob has to wait until the signal is received from Alice's box so until she's put in her coin...

and the signal has been sent he has to wait until that's happened before he puts in his coin so that his box knows what what to do that takes some finite amount of time even if the signal is traveling at the speed of light it's still going to take some time to get there so that's not going to work if we're trying to make boxes that satisfy these rules instantaneously when Bob and Alice put in their coins at exactly the same moment we want an instantaneous solution to this problem so that's never going to happen at least it's never going to happen for classical boxes if these are

### quantum

boxes if we allow them this property of### quantum

#### entanglement

so that the two boxes can be their 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 the rules the mathematical equations allow us to calculate exactly how much how much more often we can satisfy the the four rules compared to the classical case or in the classical case we can only get get it three times out of four 75% success rate### quantum

mechanics tells you that you can get roughly 85% success rate and white white 85 well that is it's just a number that the equations give you it's actually precisely more precisely it's it's a number that involves a square root of 2 we don't need to worry about that it's just approximately 85% but I will 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 a bells experiment was allowing you to do you did the equivalent measurement with two particles that were entangled and Bob and Alice were making measurements making choices about how they 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 of Einstein's hidden variables it was only if### quantum

mechanics went beyond that as Bohr suggested it did that you could do better and get 85% well as I say this was just a thought experiment for John Bell but very soon physicists realized that you could do it for real you could create two entangled particles and make the measurements and this was done it was first done in the 1970s and then more definitively in the 1980s and since then it's been done many many times in many many different ways every single time the result has been very clear the classical limit or the hidden variables limit of 75% correlation between the particles is always exceeded you get this 85% success and so this suggests that Einsteins idea that there are these things called hidden variables which fix the properties of### quantum

particles before they're measured this doesn't apply it seems that Bohr was right now this doesn't imply as you might sometimes hear that there really is some spooky action at a distance many...times when experiments like this have been done their newspaper headlines have proclaimed that Einstein has proven wrong and that spooky action at a distance is real spooky action at a distance was what I'm Stein's interpretation of

#### entanglement

involved but actually it is a better way to think about#### entanglement

to say something a little different and one way to think about it is to say that once the two boxes become entangled they are no longer separate objects so that what happens over here is completely end up of what happens over here they are in some### quantum

sense the same object and that remains the case no matter how far apart they are even if the particles that you measure were separated were on the opposite sides of a galaxy they remain in some sense a single### quantum

entity another way of thinking about that is to say that there is some kind of sharing of information between them and this is really what Popescu and and Rolex### quantum

boxes were about it was expressing this situation in terms of a kind of sharing of information 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 doesn't happen if it did happen it would violate special relativity as Einstein suggested but### quantum

mechanics tells you something else it tells you that there is this property called...### quantum

nonlocality which is very hard to find words for but that is a real property of the world so if you see headlines saying spooky action at a distance is real don't believe them now I want to come back finally to what popescu and ralick were trying to do with their boxes because one physicists yuckier Aronoff that perhaps what we're seeing here with this### quantum

nonlocality is kind of a stretching of the normal laws of cause and effect as far as special relativity will allow so that somehow### quantum

mechanics is sort of almost violating the spirit of special relativity without violating it actually in practice without actually allowing you to transmit information faster than light perhaps### quantum

mechanics is doing this you know right up to the limit of what what is physically possible well Popescu and Rowlett thought let's let's see about that can we imagine a case in which there is some kind of#### entanglement

that does better than### quantum

mechanics that does better than 85% and they thought about it and they came up with the this idea of these two boxes that they showed could have a set of rules that without violating special relativity allows you a hundred percent correlation it's physically breaking no laws let's say that we know of to have a situation like this a kind of if you like a kind of super### quantum

correlation and so the question becomes why isn't the world like this you see we often think about### quantum

mechanics as something sort...of added on or something different from classical mechanics that classical mechanics evie this sort of 75% success rate in this case