Compose different systems with each other

## Constructing composite systems

![[Pasted image 20260729215146.png]]

This definition applies to probabilistic and quantum systems.

Example:

![[Pasted image 20260729215759.png]]

![[Pasted image 20260729215837.png]]

So to apply S to A and T to B we apply SxT to AB.

If the distribution of a probabilistic system can be written as a composite A and B are independent
If we cannot they are depended on each other

If the quantum state of a system AB can be written as a tensor product they are independent
If we cannot the quantum states depend on each other, we call this entangled~

![[Pasted image 20260729220918.png]]


## Measuring composite systems

We can compose two separate measurements similarly to how we applied the tensor product.

![[Pasted image 20260729221447.png]]

Example:

![[Pasted image 20260729221513.png]]
![[Pasted image 20260729221523.png]]