- 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)
