Explore the intersection of quantum information and cryptography in this lecture from the IPAM Graduate Summer School on Post-quantum and Quantum Cryptography. Delve into how quantum communication can relax assumptions required for secure multiparty computation (MPC), allowing mutually distrustful parties to compute functions of private inputs while preserving confidentiality. Trace the evolution of this research from Crepeau and Kilian's foundational work to recent developments showing how one-way functions can imply oblivious transfer and MPC in a quantum context. Gain insights into the potential of quantum cryptography to enhance security with weaker assumptions, and understand the implications for future cryptographic systems.