# Quantum States

Until now, we have talked about quantum states informally. Sno, now let's talk about the quantum state formally and how we can represent it mathematically.

## Single qubit states

Classical bits, represented by low and high voltages in a transistor, are represented using two numbers, **0** and **1**. Quantum states are different. Instead of numbers, quantum states are represented by **vectors**. As you would recall, vectors have both **magnitude** and **direction** in space associated with them. More specifically, a quantum state is a vector in two-dimensional vector space. We will refer to this two-dimensional vector space as the **state-space** of a single qubit.

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