Explore the final part of a three-part lecture series on quantum computing, presented by Fang Song from Portland State University at IPAM's Graduate Summer School on Post-quantum and Quantum Cryptography. Delve into an alternative formalism of quantum information based on density matrices, examining concepts such as mixed states, purification, quantum channels, and POVM measurement. Gain insights into distance measures of quantum states and operators, essential for modeling and analyzing security in both post-quantum and quantum cryptography. Enhance your understanding with suggested readings from Watrous' quantum computing and quantum information notes. Recorded on July 26, 2022, this 58-minute lecture offers an advanced exploration of quantum computing principles crucial for cryptographic applications.