- Sometimes the best way to win a game
is to use quantum physics.
Game theory was invented as the study of strategies
we can use in games to get the best outcome,
then a bunch of physicists decided to join the party
and see what would happen
if we added quantum effects to the mix.
"Why would anybody want to do this?"
You may ask.
Well apart from the fact that it's cool and fun,
in a lot of cases we can actually get a better outcome,
take this classic example,
the prisoner's dilemma.
You and your friend, let's call her Dianna,
have just been caught robbing a bank.
The police bring you both in for questioning,
and place you in separate rooms.
Now a few things can happen here,
one, you both stay quiet.
- [Both] No comment.
- And the officer only has enough evidence
to put you both away for one year (door slamming).
Two, Dianna snitches on you,
and you stay quiet.
No comment.
- It was all her, I had nothing to do with it!
- [Jade] You get five years, and she goes free.
(upbeat music)
Three, you snitch on Dianna,
while she's stay quiet.
- No comment.
- It was all her, I had nothing to do with it.
She gets five years and you go free.
(muffled chatter and laughing)
Four, you both snitch on each other.
- [Both] It was all her, I had nothing to do with it.
- The officer gives you both three years
for dishonesty and being bad friends.
So what's the best thing for you to do here?
Or as they same in game theory,
what's the optimal strategy?
Well let's analyze our options, shall we.
We'll draw them up in a table,
with your jail sentence being the left number,
and Dianna's jail sentence being the right.
Now the best thing for both of you,
is to both stay quiet,
as you'll only get one year each,
but you're not playing for both of you,
you're playing for you.
If you stay quiet, Dianna might snitch on you,
and then you'd go to jail for five years!
If she stays quiet and you snitch on her,
you have a chance of getting zero jail time,
or going away for three years
if she snitches too.
Three years is better than five,
so the safest thing for you to do is snitch,
and it's exactly the same for Dianna.
Basically, no matter what the other player is doing,
you're rewarded for snitching.
This point is called the Nash equilibrium,
discovered by John Nash who won the Nobel Prize in Economics
for this very idea.
The Nash equilibrium is the point
where neither players have any incentive
to change their decision.
If you stay quiet,
you don't know whether you're in this square or this one,
so the smartest thing for you to do is snitch.
This is the catch of the prisoner's dilemma,
what's best for the individual,
isn't what's best overall.
Now, if we introduce some quantum rules,
we can actually do away with the catch,
in other words, we can guarantee
that if you both stay quiet
you won't get screwed over by the other player.
I found a science paper which outlines it perfectly,
this is how it works.
You're both given a qubit,
what's a qubit?
Qubit is short for quantum bit,
and bit is short for binary digit,
just think of bits as pieces of information,
usually represented by ones and zeros.
So like most things in the world,
bits can only be in one state at a time,
they can either be a one or a zero.
Quantum bits, qubits, can be a one and zero
at the same time.
I know this sounds weird,
but it's a phenomenon that pops up a lot
in quantum physics,
it's called superposition.
You may have heard the story of Schrodinger's cat.
A poor kitty is locked in a box
with a radioactive atom, a Geiger counter,
a hammer, and a vial of poison.
If the atom decays, the Geiger counter reacts
by triggering the hammer to smash the vial,
poisoning the cat (cat meowing),
but the decay time of the atom is totally random,
we have no way of knowing
if it's decayed yet or not,
meaning we have no way of knowing
if the cat is dead or alive.
Quantum mechanics says it's in a superposition
of being both dead and alive,
it's only when we open the box and look inside
that it collapses into
one state or the other (cat screeching).
Now imagine the cat is a qubit,
and instead of being alive and dead at the same time,
it's a one and zero at the same time.
It's not as dramatic, I know,
but the same rules apply.
It'll collapse into a one or a zero
when it's measured.
(qubit screeching)
Another thing qubits can do
is become entangled with one another.
Entanglement is another one of those things
that seem super weird to us,
but is actually pretty normal in the quantum world.
It's actually not that hard to wrap your head around
if you just forget everything you know
about how the world works.
For example, if a particle with total spin zero
decays into two spin half particles,
because of the conservation of angular momentum,
the total spin needs to be conserved,
which means that if one is spin up,
the other needs to be spin down,
but because they're quantum particles,
they can be in a superposition
of spin up and spin down until they're measured.
So if we transport one to the other side of the galaxy,
and measure the one here on Earth,
if it collapses into a spin up state,
the other one will instantaneously
collapse into spin down,
like faster than the speed of light instantaneous,
it's like it somehow knows
about the state of the other one.
This is what entanglement is,
and we can entangle qubits
so that they both collapse into the same
or opposite state when measured.
So you both have a qubit,
now in the regular, non-quantum scenario,
you only have two options,
stay quiet or snitch,
but now with your qubits,
you have a whole new range of quantum moves.
I won't go into exactly what they are here,
because it's like a lot of math,
but the authors of this paper
highlight what they call a Q move,
which ensures that you can both stay quiet,
with a guarantee that the other player won't snitch.
In other words,
the presence of the qubit forces cooperation.
- [Both] No comment.
- You still have to go to jail for a year,
but, hey, bank robbing is a crime.
So beyond getting less jail time,
what can quantum games be used for?
Well regular, classical games
have taught us a lot about computation.
By thinking of algorithms as strategies,
we can imagine their design as a game.
For example, an opponent is trying to break your algorithm,
and you have to find strategies
to make it more robust.
With the advent of quantum computers,
there's no doubt that quantum games
will help us explore the possibilities
of quantum computing.
Thanks so much for watching, guys,
and thank you to Dianna from Physics Girl
for collaborating with me on this video.
We also did a video over on her channel,
so you should definitely go check that out,
it's pretty cool,
it's about how you can stop someone cheating
by using photons.
If it's your first time here, welcome,
I make videos about physics, math, and computer science
pretty regularly, every two weeks or so.
So yeah, if that sounds like something
that would interest you,
don't forget to subscribe.
Take a look around, leave me a comment, say hi,
and yeah, bye!
(upbeat music)