Mermin–Peres square
Okay, so imagine you have two people, Alice and Bob, and they each have a box with a light inside. The light can either be turned on (1) or off (0).
The Mermin-Peres square is like a game they can play together. Alice and Bob each secretly choose whether to turn their light on or off, and then they compare notes. The goal is to get a certain pattern of lights to appear.
The pattern they want is that the total number of lights turned on is either 0 or 2 (so, either both are off, or one is off and one is on). They also want the pattern to be different every time they play the game.
Now, here's the tricky part. Alice and Bob are not allowed to talk to each other while they are making their choices. They have to decide completely independently. So how do they make sure they get the right pattern?
Well, it turns out that they can use some really cool math to figure it out. They use something called "parity", which just means whether something is odd or even.
Each time they play the game, they keep track of the parity of their own light (whether it's on or off) and then add up those two numbers. If the total is odd, they both switch their light to the opposite of what it was before. If the total is even, they both leave their lights alone.
It might seem like this wouldn't lead to the right pattern, but trust me, it works! If you try it out enough times, you'll start to see the pattern emerge. And that's the Mermin-Peres square! It's a cool mathematical way to make sure Alice and Bob "cheat" in just the right way to win the game.
The Mermin-Peres square is like a game they can play together. Alice and Bob each secretly choose whether to turn their light on or off, and then they compare notes. The goal is to get a certain pattern of lights to appear.
The pattern they want is that the total number of lights turned on is either 0 or 2 (so, either both are off, or one is off and one is on). They also want the pattern to be different every time they play the game.
Now, here's the tricky part. Alice and Bob are not allowed to talk to each other while they are making their choices. They have to decide completely independently. So how do they make sure they get the right pattern?
Well, it turns out that they can use some really cool math to figure it out. They use something called "parity", which just means whether something is odd or even.
Each time they play the game, they keep track of the parity of their own light (whether it's on or off) and then add up those two numbers. If the total is odd, they both switch their light to the opposite of what it was before. If the total is even, they both leave their lights alone.
It might seem like this wouldn't lead to the right pattern, but trust me, it works! If you try it out enough times, you'll start to see the pattern emerge. And that's the Mermin-Peres square! It's a cool mathematical way to make sure Alice and Bob "cheat" in just the right way to win the game.