In the last episodes, we dove into the fascinating world of Quantum Error Correction (check here). Today, we shift gears to explore the basic principles that are foundational to quantum algorithms and applications.

Imagine a game so simple a child could play it, yet so profound it solved the most intriguing debate across Einstein and Bohr about quantum physics. It looks like a standard cooperative puzzle, the kind you might play at a team-building retreat.

Let’s explore how a simple game helped scientists unravel one of the greatest mysteries in science!

Here is how it works. You have two players, Alice and Bob, and a Referee. It is a team game and Alice and Bob are on same team, they win or lose together.

Alice and Bob are put in separate rooms. They cannot see each other, talk, or text. The Referee randomly sends a single number—either a 0 or a 1—to Alice. He does the same for Bob.

There are four possible input pairs:

The Goal:
After receiving their numbers, Alice and Bob must each send a number (a 0 or a 1) back to the Referee. They can send whatever number they want (a 0 or a 1) but they win the round only if:

That’s the whole game. Agree three times. Disagree once.

Alice and Bob meet before the game and agree on a simple plan:

Let’s see what happens.

If the inputs are:

They win 3 out of 4 cases.

That’s 75%.

Not bad. But surely we can be smarter than that?

Maybe Alice says:

Bob could try something more subtle:

Let’s test this strategy.

Case by case:

Again: 3 wins, 1 loss. Still 75%. Can we do better?

Let's imagine you are Bob. You are sitting in your room, and the Referee hands you the number 1.

You have to make a decision. What do you send back?

Here is your dilemma: You do not know what Alice has. She might have a 0, or she might have a 1.

This is the logical trap. You only have one output. You have to send one number back. But the requirements for your two possible situations are opposites.

If you plan to match her, you win Scenario A but lose Scenario B. If you plan to mismatch her, you lose Scenario A but win Scenario B.

You can try any combination of plans you want. You can flip coins, memorize codes, or use complex algorithms. But because you don't know what the other person is holding, you will always face a contradiction in that final scenario.

Logic itself dictates that you must lose 25% of the time.

The reason behind this belief was simple: In this game, you have to plan your strategy in advance, and there’s no communication allowed once the game starts. So, your moves are entirely predetermined before the game begins.

Now let us go back to quantum physics. According to quantum theory, particles exist in superposition—meaning they are in a mixture of states (like being neither 0 nor 1 at the same time) until the moment they are measured. In this view, championed by Niels Bohr, the outcome isn't decided until the very last second. Nothing is pre-determined.

Albert Einstein hated this idea. He argued that "God does not play dice." He believed that even if we can't see them, there must be hidden instructions inside the particles—pre-determined states—that tell them what to do. In his view, the universe has a script, even if we don’t know it yet.

For decades, this was just a philosophical argument. Two geniuses talking in circles.

How do you prove who is right? Physics, after all, is an experimental science.

Then came the ingenious insight of John Bell. He realized that this simple game was the key to settling the argument once and for all.

Bell saw that if Einstein was right, if the particles really did have pre-determined hidden instructions, they would be exactly like Alice and Bob sharing a pre-determined strategy. They would be bound by the laws of logic we just walked through. They could never, ever beat the 75% win rate.

But, if Bohr was right, if the particles truly existed in superposition and shared a connection beyond classical physics, they might be able to coordinate in ways that defy the pre-determined strategy. They might be able to break the 75% win rate.

Suddenly, the stakes are huge:

Next, we’ll play the very same game again, but this time using quantum mechanics, and see not only whether Einstein or Bohr had the better intuition, but what the experimental evidence says about how the world actually works!

All of that is coming in the next post… our 25th episode. Don’t miss it!