A Partial observation is, as the name implies, only an observation of a partial aspect of the result.

First, we need to distinguish between alternatives we want to look at.
Each alternative is a set A of deterministic possibilities.
Partial observation yields for each alternative A the probability that the system is in a state in A.

![[Pasted image 20260729122658.png]]

We will often use this, less precise, definition however:

![[Pasted image 20260729122833.png]]

A partial observation of a classical probabilistic system does not change it.
An example for this:

![[Pasted image 20260729122952.png]]
![[Pasted image 20260729123015.png]]


## Partially measuring a quantum system

![[Pasted image 20260729123551.png]]
![[Pasted image 20260729123600.png]]

As with a complete measurement, the partial measurement changes the system!!
Also called "projective measurement in the computational basis"

Example:
![[Pasted image 20260729124711.png]]
![[Pasted image 20260729124718.png]]
