Quantum Computing tutorial | Part 2.1: Mixed states for Quantum Information Theory скачать в хорошем качестве

Quantum Computing tutorial | Part 2.1: Mixed states for Quantum Information Theory

Part 2.1 of the Quantum Computing tutorial. Covering UvA Quantum Information Theory course Lecture 1-3 content (without properties, proofs, exercises), taught in 2025 Fall: 1. States as density matrices 2. Hermitian, inner product, outer product operations 3. Hermitian eigendecomposition 4. Matrix singular value decomposition 5. Reduced states via partial trace 6. Mixed state standard purification 5. Pure state Schmidt decomposition 7. (Standard) Maximally entangled state 8. Measurement Upcoming in the next tutorials - the rest of UvA Quantum Information Theory: 1. Shatten norms, trace distance, fidelity, quantum channels (CPTP maps) 2. Choi operator, Kraus representation, Stinespring representation 3. Shannon entropy, Von Neumann entropy 4. Quantum codes and compression 5. Mutual information, data processing inequality 6. Holevo bound, relative entropy 7. LOCC and separable channels 8. Nielsen's theorem, distillable entanglement, entanglement cost 9. Tensor networks You can find the full video whiteboard here: https://www.npw.lt/assets/files/yt-2.... Sources: Lectures Notes on Quantum Information Theory Michael Walter and Maris Ozols, University of Amsterdam, 2025 --- 00:00 Introduction 02:57 Single system and it's state (pure, mixed), Bloch sphere; Hermitian, inner product, outer product 14:57 Composite system and it's state (product, separable, entangled) 19:39 Reduced state (partial trace) 29:14 Purification (reverse reduction) 37:50 Intuation behind reduction, standard purification, Schmidt decomposition 39:08 Schmidt decomposition 39:51 Singular value decomposition 46:28 Measurement 57:24 Outro