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Purifications and Fidelity | Understanding Quantum Information and Computation - Lesson 12

This lesson explores the concept of a purification in quantum information, where an arbitrary quantum state is represented by a pure state of a larger system that leaves the original state when the rest of the larger system is discarded. This is an incredibly useful concept that allows us to reason interesting things about density matrices by essentially viewing them as parts of pure states, which are simpler in some respects. The lesson also introduces fidelity, a measure of similarity between two quantum states, which plays a key role in quantum computing. Along the way we'll also discuss Schmidt decompositions, the unitary equivalence of purifications, and Uhlmann's theorem, which links fidelity to purifications. 0:00 — Introduction 1:29 — Overview 2:23 — Purifications 4:02 — Existence of purifications 7:33 — Schmidt decompositions 12:54 — Unitary equivalence of purifications 16:21 — Example: superdense coding 18:04 — Cryptographic implications 20:47 — HJW theorem 25:48 — Definition of fidelity 31:32 — Properties of fidelity 35:24 — Gentle measurement lemma 39:18 — Uhlmann’s theorem 43:45 — Conclusion Find the written content for this lesson on IBM Quantum Learning: https://learning.quantum.ibm.com/cour... #ibmquantum #qiskit #learnquantum