In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state.

The term “state preparation procedure” is widely used in quantum mechanics without clear explanation of what it is or isn’t. Sometimes it’s suggested that it is a controlled procedure in a laboratory.

On the other hand, measurement in quantum mechanics is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic.

The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.

In summary, state preparation in quantum mechanics refers to the process of preparing a system in a specific quantum state, while measurement refers to the process of obtaining information about the system by performing an experiment on it. The two concepts are related because the state of the system determines the probabilities of obtaining different measurement outcomes.
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