diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 99a58a7..38a877e 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -216,6 +216,8 @@
   },
   "active": "25f5b25d5eca7203",
   "lastOpenFiles": [
+    "SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164820.png",
+    "SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164547.png",
     "SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728163713.png",
     "SS2026/Quantum Computing/2. Probabilistic systems/Anhänge",
     "SS2026/Quantum Computing/1. Introduction/Introduction.md",
@@ -247,8 +249,6 @@
     "SS2026/Datenbanken und Informationssysteme/8. Alternative Datenmodelle und No-SQL/Anhänge/Pasted image 20260723201457.png",
     "SS2026/Datenbanken und Informationssysteme/8. Alternative Datenmodelle und No-SQL/Anhänge/Pasted image 20260723200735.png",
     "SS2026/Datenbanken und Informationssysteme/9. RDF und Semantic Web/Anhänge",
-    "SS2026/Datenbanken und Informationssysteme/7. Transaktionsverwaltung/Anhänge/Pasted image 20260723185939.png",
-    "SS2026/Datenbanken und Informationssysteme/7. Transaktionsverwaltung/Anhänge/Pasted image 20260723185557.png",
     "SS2026/Datenbanken und Informationssysteme/4. SQL/Unbenannt.md",
     "SS2026/Datenbanken und Informationssysteme/4. SQL/TCL Transaction Control Language SQL.md",
     "SS2026/Datenbanken und Informationssysteme/4. SQL/DQL Data Query Language SQL.md",
diff --git a/SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164547.png b/SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164547.png
new file mode 100644
index 0000000..0602d9f
Binary files /dev/null and b/SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164547.png differ
diff --git a/SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164820.png b/SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164820.png
new file mode 100644
index 0000000..0aeb2cc
Binary files /dev/null and b/SS2026/Quantum Computing/2. Probabilistic systems/Anhänge/Pasted image 20260728164820.png differ
diff --git a/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md b/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md
index 55e2fde..36fe872 100644
--- a/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md	
+++ b/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md	
@@ -13,4 +13,11 @@ For a coin flip the probability distribution would be $d_coin \in \mathbb{R}^2$
 A probabilistic process is a Matrix A $\in$ $\mathbb{R}^{N \times N}$ if every column of A is a valid probability distribution.
 ![[Pasted image 20260728163713.png]]
 An example for generating a 2 bit number and then using a bit flip device to flip both 
-bits with a probability of 1/3 
\ No newline at end of file
+bits with a probability of 1/3 
+For two zeroes this results in 1/3 chance to get 11 and 2/3 chance for nothing to happen.
+Here, A would look like this:
+![[Pasted image 20260728164547.png]]
+
+### Applying a probabilistic process
+A Process A applied to a distribution x is defined as Ax.
+![[Pasted image 20260728164820.png]]
\ No newline at end of file