Carl Miller, a mathematician at NIST, shares his journey from pure mathematics to quantum information science. He found the field challenging and fun because it requires revising foundational assumptions based on developments in other fields. At the subatomic level, quantum phenomena like superposition and entanglement challenge classical logic and probability.
Miller illustrates this with a Magic Square game puzzle. Alice and Bob must fill in a grid to satisfy three conditions without communication. Using entangled particles and linear operators, they can win the game every time, but the outcome remains inherently unpredictable. This demonstrates how quantum mechanics can “undo” mathematical proofs based on classical assumptions.
Miller and Yaoyun Shi proved that untrusted devices can simulate partially trusted ones, creating “certified randomness” with today’s technology. This has implications for cryptography, as quantum computers threaten existing encryption schemes. Miller works on NIST’s Post-Quantum Cryptography project, designing next-generation standards resistant to quantum attacks.
The field of quantum information science is rapidly evolving, with large companies competing to build quantum computers and quantum cryptographic solutions becoming available to the public. This presents many new mathematical challenges and opportunities for applied mathematicians like Miller.
Source: https://www.nist.gov/blogs/taking-measure/quantum-information-changing-rules-game
Keywords: Quantum Superposition, Certified Randomness, Entanglement, Quantum Logic, Quantum Algorithms
