4 Nonlocal games: Working with multiple qubits

In the last chapter, we used qubits to communicate with Eve securely, exploring how we can use quantum devices in cryptography. Working with one qubit at a time is fun, but working with more will be—well, more fun! In this chapter, we’ll learn how to model states of multiple qubits and what it means for them to be entangled. We will again be playing games with Eve, but this time we will need a referee!

4.1 Nonlocal games

At this point, we have seen how single-qubit devices can be programmed to accomplish useful tasks such as random number generation and quantum key distribution. The most exciting computational tasks, however, require using multiple qubits together. In this chapter, we’ll learn about nonlocal games: a way to validate our quantum mechanical descriptions of the universe with friends using multi-qubit systems.

4.1.1 What are nonlocal games?

We have all played games of one type or another, whether sports, board games, video games, or role-playing games. Games are one of the best ways to explore new worlds and test our limits of strength, endurance, and understanding. Turns out Eve loves to play games, and the latest encrypted message from her was the following:

4.1.2 Testing quantum physics: The CHSH game

4.1.3 Classical strategy

4.2 Working with multiple qubit states

4.2.1 Registers

4.2.2 Why is it hard to simulate quantum computers?

4.2.3 Tensor products for state preparation

4.2.4 Tensor products for qubit operations on registers

Summary