From 0f230a29dd6204b51df064830c1e07236e36cea6 Mon Sep 17 00:00:00 2001 From: Benjamin Neumann Date: Tue, 28 Jul 2026 16:27:30 +0200 Subject: [PATCH] vault backup: 2026-07-28 16:27:30 --- .../2. Probabilistic systems/Probabilistic Systems.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md b/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md index 51c6c19..acdf7d0 100644 --- a/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md +++ b/SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md @@ -4,6 +4,10 @@ All the different possible outcomes. ### Probability distribution A Probability for each possibility: Pr[x] = p where p $\in$ [0,1] -`For a coinflip this would be Pr[Heads] = 1/2 and Pr[Tails] = 1/2` +`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 $d_i \geq 0$ \ No newline at end of file +A valid distribution d has $\sum d_i = 1$ and for all i is $d_i \geq 0$ +For a coin flip the probability distribution would be $d_coin \in \mathbb{R}^2$ with $d = (1/2, 1/2)^t$ + +### Probabilistic processes +A probabilistic process is a Matrix A $\in$ $\mathbb{R}^{N \times N}$ if every column of A is a valid probability distribution \ No newline at end of file