diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index d0deb51..4635a3b 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -216,6 +216,7 @@
   },
   "active": "25f5b25d5eca7203",
   "lastOpenFiles": [
+    "SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730154444.png",
     "SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730153305.png",
     "SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730145119.png",
     "SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730144713.png",
@@ -233,7 +234,6 @@
     "SS2026/Quantum Computing/8. Ket Notation/Anhänge/Pasted image 20260730102305.png",
     "SS2026/Quantum Computing/8. Ket Notation/Anhänge/Pasted image 20260730102024.png",
     "SS2026/Quantum Computing/8. Ket Notation/Anhänge/Pasted image 20260730101723.png",
-    "SS2026/Quantum Computing/8. Ket Notation/Anhänge/Pasted image 20260730101435.png",
     "SS2026/Quantum Computing/8. Ket Notation/Anhänge",
     "SS2026/Quantum Computing/8. Ket Notation",
     "SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md",
diff --git a/SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730154444.png b/SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730154444.png
new file mode 100644
index 0000000..58e673c
Binary files /dev/null and b/SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730154444.png differ
diff --git a/SS2026/Quantum Computing/Bernstein-Vazirani/Bernstein-Vazirani Algorithm.md b/SS2026/Quantum Computing/Bernstein-Vazirani/Bernstein-Vazirani Algorithm.md
index c7ee826..a770d7d 100644
--- a/SS2026/Quantum Computing/Bernstein-Vazirani/Bernstein-Vazirani Algorithm.md	
+++ b/SS2026/Quantum Computing/Bernstein-Vazirani/Bernstein-Vazirani Algorithm.md	
@@ -31,3 +31,14 @@ It can be calculated as follows:
 
 ![[Pasted image 20260730153305.png]]
 
+And we can rewrite $U_f(\ket{x} \otimes \ket{-})$ as
+
+![[Pasted image 20260730154444.png]]
+
+The bottom wire has not changed.
+The top wire now has f(x) encoded in its quantum state.
+The phenomenon that the output of f is encoded as a -1 is called phase kickback.
+We need one final step before measuring.
+
+
+Now, we perform one final hadamard gate on the top wire.