Quantum Pseudorandomness in Algorithmica, and Its Implications to Cryptography and Complexity

Explore the concept of quantum pseudorandomness in Algorithmica and its far-reaching implications for cryptography and complexity theory in this 46-minute lecture by Luowen Qian from Boston University. Delve into the fascinating world of pseudorandom quantum states (PRS) and their ability to mimic Haar random quantum states against efficient distinguishers. Discover how the existence of PRS is separated from post-quantum one-way functions and even fundamental complexity class separations. Learn about the "hardness of shifted Forrelation" property in cryptographic hash functions and its significance in constructing single-copy-secure PRS. Examine the potential for realizing quantum computational cryptography from weaker assumptions than one-way functions, and consider the need for a theory of quantum meta-complexity to study the foundations of quantum computational cryptography.