vault backup: 2026-07-29 11:08:22

SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md

@@ -3,7 +3,7 @@ All the different possible outcomes.
 `Random two bit number has deterministic possibilities 00, 01, 10, 11.`
 
 ### Probability distribution
-A Probability for each possibility: Pr[x] = p where p $\in$ [0,1]
+A Probability for each possibility: Pr\[x] = p where p $\in$ \[0,1]
 `For a coin flip this would be Pr[Heads] = 1/2 and Pr[Tails] = 1/2`
 Combine all probabilities for all possible outcomes as vector to get probability distribution+
 A valid distribution d has $\sum d_i = 1$ and for all i is $d_i \geq 0$ 

SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md

@@ -65,6 +65,23 @@ After measuring we get the following distribution:
 
 
 Now, what happens if there is a bomb:
+We effectively measure if the photon took the up/down path.
+Pr\[up] = Pr\[down] = ($\frac{1}{\sqrt{2}}$)^2 = $\frac{1}{2}$
+If the photon is in the down state the bomb explodes.
+If the photon is in the up state $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ post-measurement after no explosion it reaches the second splitter after which it is in the state B$\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ = $\begin{pmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}$  
+This leads to the following probability distribution:
+![[Pasted image 20260729110112.png]]
+
+Now, from this we can see that if the photon arrives in the down state,
+there must be a bomb present!
+
+Still, we have a 50% chance of getting blown to smithereens xd
+BUT having a 25% chance to observe a bomb without the photon touching it is impossible classically!!
+
+This setup can be improved (to much physics) to achieve the following distribution:
+![[Pasted image 20260729110515.png]]
+
+
 
 
 

SS2026/Quantum Computing/Introduction to Quantum Computing.md

@@ -1 +1,5 @@
-1. [[Introduction]]
+## 1. [[Introduction to Quantum physics]]
+## 2. [[Probabilistic Systems]]
+## 3. [[Quantum Systems]]
+## 4. [[Observing probabilistic and measuring quantum systems]]
+## 5. [[Partial observing and measuring systems]]