[MUSIC PLAYING] Hey, y'all.

I'm Dianna.

You're watching "Physics Girl," and I want to tell you about a well-known problem in the field of quantum cryptography.

The problem is basically flipping a coin over the phone, but let's see why that might cause problems.

Hey Jade.

Hey.

Are we still on for the Beyonce concert Friday night?

That's the same night as the Starset concert.

JADE (ON PHONE): Oh, well, what if we flip a coin?

If it's heads, we got to Beyonce.

And if it's tails, we go to Starset.

OK.

I'll flip it.

JADE (ON PHONE): OK.

But let's Facetime so I know you're not cheating.

DIANNA (ON PHONE): Ooh, my phone's going to die.

I can't.

OK. Fine.

Looks like it landed on tails.

Starset, here we come.

Oh, it totally did not land on tails.

You just-- You just love Beyonce.

You always do this.

We always just end up doing what you-- 32 00:00:42,173 --> 00:00:42,960 You see?

But we could do a quantum coin flip, which is the obvious solution for a situation like this between two parties who don't trust each other.

A quantum coin flip goes like this.

First, we need to a basic principle of quantum physics known as wavefunction collapse, which states that measuring a quantum object, like a tiny particle, changes it.

For example, photons, the particles of light, have a quantum property called polarization.

Polarization is like light's orientation.

Because yes, light travels in a direction, but it also waves in a direction.

Like, it can wave up and down, but it can also wave side to side and diagonally.

And the direction of waves is the polarization.

Guess what direction normal light, like light from sunlight or from a lamp is polarized?

Trick question.

It's unpolarized because it has waves of all different and random polarizations mixed together.

But we can make light wave in one particular direction by passing it through a filter.

Like, pass it through a vertical filter, and it'll come out waving up and down.

But if we try to pass light that's already vertically polarized through a horizontal filter, it will be blocked.

Photons can't pass through filters that are at 90-degree angles to their polarization.

However, and this is the interesting part, if we try and pass a photon through a filter with a 45 degree of difference, like, vertical to diagonal, something weird happens.

Half of the time it goes through, and half the time it gets blocked.

And there's no way to predict which it will do.

It's completely random.

And the photos that make it through are now diagonally polarized, which means the act of measuring the light's polarization changes It.

That is wavefunction collapse.

And it can be demonstrated using polarizing filters in a demo that has blown many a mind, including mine.

Check it out.

Vertical polarizing filter.

Sunlight goes through.

Horizontal filter, all the light is blocked.

But when I add a diagonal filter in between, some light can make it through.

This is the weird thing about quantum objects they act based on probabilities.

So when the vertically polarized photons come the diagonal filter, they act completely based on chance.

So half of them make it through and half of them don't.

The ones that make it through are now diagonally polarized.

And so now when those get to the horizontal filter, they're again at a 45-degree angle.

So now again, half of them make it through.

So cool.

Now we can use this wacky property of photons to make sure no one cheats.

This is what's going to happen.

Dianna is going to choose one type of orientation, vertical and horizontal, which is called rectilinear, or diagonal.

Then, using only that orientation, she's going to send me a stream of photons, which will encode a random sequence of ones and zeros.

I'm going to record these ones and zeros and try and guess which orientation she chose.

If I'm right, I win.

If I'm wrong, she wins.

Here's an example.

OK. Say I choose the rectilinear measurement orientation.

Don't tell Jade.

So I only use the vertical and horizontal filters on my photons.

Now I make a random sequence of ones and zeros on my computer and then I encode, or match, these ones and zeros into photons by saying a vertically polarized photon means a one and a horizontally polarized photon means a zero.

And finally, I'll send my photons off to Jade via a secure channel.

Jade, I'm sending you some photons.

OK.

I've polarized them so that these, the vertical and first diagonal, are.

ones.

And these, the horizontal and the other diagonal, are zeros Wait.

How will I know which filter to use?

You won't.

Jade doesn't know which orientation I chose, so she alternates randomly between using a rectilinear and a diagonal filter.

When she measures a vertical photon with a vertical filter, it passes through and she notes down a one.

When it's a horizontal photon and it gets blocked, she writes down a zero.

But when she uses a diagonal filter to measure a vertical photon, there's a 50/50 chance it gets blocked.

And when that happens, she has no way of knowing if it was vertical, horizontal, or just the wrong type of diagonal.

But because it gets blocked, she notes down a zero.

The same thing could happen with a horizontal photon.

It could go through, and in that case she would wrongly note down a one.

JADE (ON PHONE): OK.

I've recorded them all and noted them down in separate tables.

DIANNA (ON PHONE): OK.

Guess whether I've polarized them using a rectilinear or a diagonal filter?

Her recordings don't give away any information as to which orientation I chose.

So just like heads or tails, she has a 50/50 chance of getting it right.

JADE (ON PHONE): Uh, diagonal?

Ha.

No.

It was rectilinear.

Oh you totally just cheated again.

How am I supposed to believe you?

You just-- Now to prove that I'm not cheating, I just read out my sequence of ones and zeros.

It should match exactly what Jade got in her rectilinear side of the table.

If we imagine for a second that she correctly guessed rectilinear and I tried to cheat by saying it was diagonal, which, of course, I would never do, I would have to guess all the ones and zeros in the diagonal column, and I'd have to get those correct.

But if we used enough photons, that would be pretty much impossible.

OK, here it goes.

One, zero, one zero, zero, zero, one, one, one, one, zero, one.

It's rigged.

I'm staying home Friday night.

As Jade knows, because she's also a physicist, there's no way to rig this system.

It was just an unfortunate outcome.

Happy physicsing.

I'm going to go enjoy a concert.

[MUSIC PLAYING] Should have come to the concert, Jade.