Entanglement is a unique form of correlation that exists only in quantum mechanics and
it has such profound implications that people such as Albert Einstein had really trouble
believing that quantum mechanics was complete because once you understand this property
of entanglement, you find out that it leads to things that he called for example, the
spooky action at a distance, when the action in one place instantly inferences what happens
in another place. And it also leads to having systems that lose their individuality, but
only exist in relation with each other. Like two people of the opposite gender, not having
a gender of their own, but only being defined as being the opposite until you go and check
what their gender is. I'm not going to be able to really explain what entanglement is
but what I will try to do is to explain what it is not. It is not just a form of correlation.
And to explain that, I have prepared for you a simple piece of paper where I have written
in blue a plus one on the left, and a minus one on the right. So these numbers are anti-correlated,
they are the opposite of each other. And then on the back side of the paper, in red, I have
also written anti-correlated numbers, a minus one and a plus one. What I can do now is to
break this piece of paper and fold it and pretend I haven't seen what numbers are on
it, and for example, I could give the right hand side of the paper to some other person
who is catching a plane to a distant city and agree that tomorrow night at midnight,
each one of us looks at what numbers are on our piece of papers. So tomorrow night, at
exactly midnight, I could take my piece of paper and read the blue side and find there
is a plus one on here. I now instantly know, that the other person that could be on another
continent, has a minus one written in blue on his piece of paper. Now, does this violate
relativity, does this cause some conceptual problem? Well no, because the information
is not in these numbers. The information is in the correlation. The reason why I know
that there is a minus one on the other person's paper, is because I know that the numbers
are anti-correlated, but that knowledge was already with me. It wasn't transmitted faster
than the speed of light from the other person to me. So that's all perfectly fine but quantum
entanglement goes beyond this, and the only way to explain that is to show that classical
entanglement or base something called Bell's inequality. John Bell was a famous quantum
theorist who came up with a simple proof to show how different from classical correlations
the quantum entanglement is. What you need to do is simply this; calculate this quantity
that I call M, that is the product of all the pairs of numbers on that piece of paper,
on the left and on the right, in red and in blue. But the second one here has a minus
sign in front, so you can rewrite this formula as the left red multiplies the right red minus
right blue plus left blue then multiplies right red plus right blue. And from this,
it should be easy to see that there's only two possibilities. If the numbers on the right
hand side of the card on the red and the blue side, are the same, then this is zero. But
if they are the same, it means that either both plus one or both minus one, then this
must be plus two or minus two. And then this can be plus or minus one so in total, you
will get plus two or minus two out of this.
And the same happens if the two numbers are opposite, then this will be zero, and this
will be either plus two or minus two. And so again, you get plus two or minus two from
the whole formula. So no matter what choice you make for the type of correlation and no
matter how many times you repeat the generation of these numbers, you can certainly know that
the average value of this quantity will be some number that's between minus two and plus
two. So this is called Bell's inequality. This is all very simple, but if you take quantum
entangled particles, you'll find that depending on how you observe them, you can get a number
that is between 2.8 and minus 2.8.
Now, I want you to take a really deep look at this simple formula and try and imagine,
how do you get a number larger than 2 from this? If all you have is products of plus
one and minus one. You really have to think outside the box here. The only way to do it
is if the numbers on the right hand side of the card are not prewritten there. They don't
preexist but they are correlated to the number on the left hand side of the card and they
depend on whether I'm reading the red or the blue side of the card. In other words, if
I decide to take my card on the left hand side and read the red side of the card, these
numbers might be for example, opposite. So this becomes a positive number. Whereas if
I decide to read the blue side, then these numbers would become the same and then this
is also a positive number and overall, I get a number larger than plus two.
So this is essentially how you get one, the nonlocality of quantum mechanics. The numbers
that appear on the right hand side of the card depends on which side of my card I decide
to read. That's the spooky action at a distance. Two, the correlation is already there but
the numbers are not prewritten. There is no number written on these cards until I decide
to read my card, at which point a number appears and a correlated number will appear on the
other side of the card. But which number appears depends on which side I've decided to read.
This only exists in quantum mechanics and in one of the most profoundly important properties
of quantum physics, that is that the basis of a lot of quantum technologies such as quantum
communication and quantum computation.