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Partial observing and measuring/Partial observing and measuring systems.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "Observing probabilistic and measuring quantum systems" + "title": "Partial observing and measuring systems" } } ] @@ -38,23 +38,8 @@ "icon": "lucide-file-text", "title": "Introduction-to-Quantum-Computing" } - }, - { - "id": "1e162c9c3673c5c0", - "type": "leaf", - "state": { - "type": "markdown", - "state": { - "file": "SS2026/Quantum Computing/1. Introduction/Introduction.md", - "mode": "source", - "source": false - }, - "icon": "lucide-file", - "title": "Introduction" - } } - ], - "currentTab": 1 + ] } ], "direction": "vertical" @@ -229,11 +214,19 @@ "obsidian-git:Open Git source control": false } }, - "active": "1e162c9c3673c5c0", + "active": "25f5b25d5eca7203", "lastOpenFiles": [ "SS2026/Quantum Computing/Introduction to Quantum Computing.md", - "SS2026/Klausurplan.canvas", + "SS2026/Quantum Computing/5. 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Introduction/Introduction.md rename to SS2026/Quantum Computing/1. Introduction/Introduction to Quantum physics.md diff --git a/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md b/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md index 36fe872..f611252 100644 --- a/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md +++ b/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 $d_i \geq 0$ diff --git a/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729110112.png b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729110112.png new file mode 100644 index 0000000..b503d2d Binary files /dev/null and b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729110112.png differ diff --git a/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729110515.png b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729110515.png new file mode 100644 index 0000000..95bfabe Binary files /dev/null and b/SS2026/Quantum Computing/4. Observing and measuring/Anhänge/Pasted image 20260729110515.png differ diff --git a/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md b/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md index b97b697..ccc6b60 100644 --- a/SS2026/Quantum Computing/4. Observing and measuring/Observing probabilistic and measuring quantum systems.md +++ b/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]] + + diff --git a/SS2026/Quantum Computing/5. Partial observing and measuring/Partial observing and measuring systems.md b/SS2026/Quantum Computing/5. Partial observing and measuring/Partial observing and measuring systems.md new file mode 100644 index 0000000..e69de29 diff --git a/SS2026/Quantum Computing/Introduction to Quantum Computing.md b/SS2026/Quantum Computing/Introduction to Quantum Computing.md index 6f90b8b..4edcccc 100644 --- a/SS2026/Quantum Computing/Introduction to Quantum Computing.md +++ b/SS2026/Quantum Computing/Introduction to Quantum Computing.md @@ -1 +1,5 @@ -1. [[Introduction]] \ No newline at end of file +## 1. [[Introduction to Quantum physics]] +## 2. [[Probabilistic Systems]] +## 3. [[Quantum Systems]] +## 4. [[Observing probabilistic and measuring quantum systems]] +## 5. [[Partial observing and measuring systems]]