Understanding Quantum Entanglement – with Philip Ball

September 21, 2019 0 By Kody Olson

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.