I've gone through a number of Lenny Susskind's lectures on entanglement (both just for the joy of it and to better understand quantum mechanics) where he delves into the idea of a qubit.

For the sake of this example, let's go with the magnetic moment of an electron which can be 0 or a 1 at measurement. I'll go with 2 qubits alongside the classical model as a comparison.

**Classical Bit Model**

A two bit system (00, 01, 10, 00) has for possibilities and can be described using **2 bits** of information.

**Qubit Model**

The Qubit model consists of the following:

```
a|00>
b|01>
c|10>
d|11>

a|00> + b|01> + c|10> + d|11> = 1

```

Where `a|00>`, `b|01>`, `c|10>`, and `d|11>` squared are complex amplitudes representing the probabilities of each state at measurement respectively. In this case, there are **4 bits** of information required to describe this system.

Subsequently, a 3 bit system would require **8 bits** of information (2^3) to describe.

**Entanglement** refers to the fact that **both bits** are described by **one** wave function when calculating the probabilities of each outcome. They no longer vary independently.

**Superposition** refers to the idea that the system is a linear combination of each state (akin to northeast in comparison to north and east separately) until the system is measured; after which it collapses into a single defined and possible state.

---

The classical model requires `n bits` to describe a system of `n bits`, whereas a quantum mechanical model requires `2^n bits` to describe a system of `n bits`.

Thus, a quantum computer requires an exponential amount of information to describe its state in comparison to an equivalent classical computer of the same bit number.