# 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, and 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 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 Rohrlich. 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, 2 electrons. And 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 2 values. It’s a bit like a sort of

quantum heads or tails. An 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 2 states of electrons in some ways, it’s a bit like having 2 gloves,

a left-handed and a right-handed glove. Now, if you imagine

that you have those 2 gloves, and you send them out to 2 people

on different sides of the world, maybe. And these 2 people

– we’re going to meet them again shortly – are called

Alice and Bob. Amm… 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 2 entangled photons {electrons},

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’s spin. So that once Alice had found

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’s spin,

to make sure that it was spin down. Alice could equally

have measured her electron and found that it had spin down,

in 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,

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 span 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 2 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 and the right-handed glove,… which were left-handed and right-handed

all along, in transit. So, there were

these 2 possibilities for what entanglement was about,

Bohr’s view and Einstein’s 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 exist between the spins

of the 2 entangled electrons. How do we know if that’s due to hidden variables,

or due to something else, that Bohr was suggesting? That changed 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 2 possibilities. And it’s John Bell’s experiment that these boxes,

these quantum boxes, are mimicking. Personally, I’ve never seen

an explanation of John Bell’s experiment that is at all easy to follow. So, instead of trying to

explain John Bell’s experiment, that’s what these boxes are for. So, here’s how

this box analogy works. There are these 2 boxes. They are machines,

slot machines, into which you can put a coin

and get out a toy. So you can put it in either… they will take

either 1-pound coins or 2-pound coins. And out will come one of 2 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 coin,… then you will get out a

certain animal, OK? We have to figure out combinations of which coins

give which kind of animals, in order to satisfy 3 rules. And 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 Bell’s experiment. And the rules go as follows. 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

1 rabbit and 1 dog. And it doesn’t matter

which way ’round that is, but they will have

that combination. The third rule is that

any other combination of coins, other than two 2-pound coins,.. will produce

either 2 rabbits or 2 dogs. So we have to find

inputs and outputs that satisfy these 3 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 1-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 1-pound or 2-pound –

Bob puts into his box, it has to produce also a rabbit. That’s because, if Alice has produced

a rabbit with 1 pound, then the only way

we can get a dog is that

if they both put in 2 pounds. So Alice already put in 1 pound. So, Bob’s box has to produce a rabbit

in both of those cases, with a 1-pound

or a 2-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 2-pound coin in Alice’s box will produce. Well, let’s think about it. If she puts in a 2-pound,

Bob puts in a 2-pound, too. We’ve also got the second rule,

which says that two 2-pound coins have to produce

a rabbit and a dog. So that must mean

that a 2-pound in Alice’s box produces a dog. And then we’ve satisfied

the second rule. The trouble with that is that those [outputs]

inputs and outputs violate the rules

in another case. Because for a 1-pound

and a 2-pound, we’ve got this combination

of rabbit and dog. But we’re only meant to get that

if they both put in 2 pounds. So in one time,

out of the 4 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 3 times out of 4. Now, if you think

that you have found a solution that satisfies these 3 rules

all the time, in all 4 cases, it’s probably 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 hat does that, that 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 allow that to happen,

which is that we produce a physical connection between the boxes,

that sends a signal between them. So that 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, or 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 to do. That takes some

finite amount of time. Even if the signal is travelling

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 {2 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 rules,

the mathematical equations — allow us to calculate

exactly how much more often we can satisfy the…the 4 rules,

compared to the classical case. So, in the classical case, we can only get…

get it 3 times out of 4, 75% success rate. Quantum Mechanics tells you

that you can get roughly 85% success rate. And why… why 85? Well, that is… is just a number

that the equations give you. It’s actually,

more precisely, it’s, ahh,… it’s a number that involves

the square root of two. 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 Bell’s experiment was allowing you to do. You did

the equivalent measurement with 2 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 realised

that you could do it for real. You could create 2 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 Einstein’s 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, the newspaper headlines

have proclaimed that Einstein is proven wrong, and “spooky action at a distance” is real. Spooky action at a distance was

what Einstein’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 2 boxes become entangled, they are no longer

separate objects! So that what happens over here is completely independent

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 the 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 Rohrlich’s

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 Rohrlich

were trying to do with their boxes. Because one physicist, ahh,…

Yakir Aharonov, suggested, umm…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. umm… 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 is physically possible. Well, Popescu and Rohrlich thought, 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 this idea of these two boxes, that, they showed, could have a set of rules

that, without violating special relativity, allows you a 100% correlation. It’s physically breaking no laws, let’s say, Ahh… 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. Classical Mechanics give you

this sort of 75% success rate in this case. Quantum Mechanics

does something more. So we kind of think, you know,

where does that come from? Why does Quantum Mechanics

allow you to do these things that you can’t do classically? Popescu and Rohrlich approached it

from another angle. Because they showed, that actually things could be,

even, if you like, MORE quantum than they are. And so why aren’t they? And so, that raises

a new question. If we could understand

why Quantum Mechanics is limited in what quantum

nonlocality can do, — limited to this 85% figure, instead of 100% — if we could understand that,

then maybe we would understand

a little more about why it is that the world

has these quantum properties that it seems to have

at the level of fundamental particles. If you still find this analogy

a little bit confusing, then probably

what you need to do is to look it up in

my book, “Beyond Weird”, which talks

about this and more, and goes into more detail

about what quantum entanglement does and doesn’t mean,

and also about how we’re starting to make use of it

in quantum technologies, like quantum computing,

and quantum cryptography. And let me remind you,

if you haven’t already subscribed to

the Ri YouTube channel, then you should do that.