Definitions

Let's start by getting some basic definitions out of the way. The word experiment is used in probability theory to denote the execution of a procedure that produces a random outcome. Examples of experiments are flipping a coin or rolling dice. In quantum computing, an experiment is measuring a qubit.

A sample space is the set of all possible outcomes of an experiment. It is usually denoted by Ω (the upper case Greek letter omega). The set Ω for a fair coin is {Heads, Tails}. The set Ω for one die is {1, 2, 3, 4, 5, 6}. The set Ω for a qubit when measured in the Z basis is {|0⟩, |1⟩}.

An event (E) is a subset of Ω. Every outcome is a subset of size 1 – for example, {Heads} and {Tails} are events for a fair coin. But as we saw in Chapter 3, Foundations, subsets also include the empty set ∅ and the whole set itself, which is Ω in this case. The set of all events is called an event space and is usually...