COMS 6998: Quantum Cryptography (Fall 2025)

Time: Fridays 2:10-4:00

Location: TBD

Instructor: James Bartusek

Description: This is a graduate-level topics class centered around the cryptographic applications of quantum information. The first proposals for how to use quantum information in a cryptographic context were presented in a paper written by Stephen Wiesner right here at Columbia in 1968 (Conjugate Coding). It has since become clear that quantum information has remarkable cryptographic properties, exemplified by applications such as information-theoretically secure key distribution, unclonable banknotes, and computationally-secure cryptography even in a world where P=NP. This course will take a deep dive into the properties of quantum information that make this possible, and cover several prominent applications, including highlights from a recent surge of research activity at the nexus of quantum information and cryptography. 

Prerequisites: A course in either cryptography (COMS 4261 or equivalent) or quantum information (COMS 4281 or equivalent) -- ideally some familiarity with basic concepts in both areas. The quantum information will be introduced very quickly, so if you are brand-new to quantum information, I would encourage you to spend some time with the resources linked below before / during the first couple weeks of class.

Grading: Based on a few (likely 2-3) problem sets, a final reading / research project, and (potentially) scribe notes / participation. 

A selection of related courses:

• Anand Natarajan and Vinod Vaikuntanathan's course at MIT (2024) 

• Umesh Vazirani and Fermi Ma's course at Berkeley (2023)  

• Dakshita Khurana's course at UIUC (2022) 

• Henry Yuen's course at Columbia (2022) 

• Mark Zhandry's course at Princeton (2018) 

• Thomas Vidick's course at Caltech (2016) 

Quantum information resources:

• Scott Aaronson's lecture notes (Lectures 1-6)

• John Watrous' course notes (Lectures 1-4 and 9, with accompanying videos)

• Nielsen and Chuang's textbook, chapters 1-2

Schedule (subject to change)

The course will roughly be split into the following units.

• BB84 states and applications, e.g. quantum key distribution, unclonability, revocability, and blind / verifiable delegation

• Quantum cryptography with classical communication, e.g. remote state preparation, tests of quantumness, and classical verification of quantum computation

• Coset states and applications, e.g. publicly-verifiable quantum money, copy-protection, and quantum obfuscation

• Haar-random states and applications, e.g. quantum pseudorandomness and "microcrypt"