Infinite Randomness Expansion with a Constant Number of Devices
summary
Claims an unbounded (infinite) certified randomness expansion starting from a constant m‑bit seed (m ~ 100–1000), by alternating a VV exponential-expansion subroutine (m → 2^m bits) with a RUV-style extractor step that performs randomness laundering. Security relies on multi-game CHSH rigidity to certify ideal measurements on EPR pairs and on an input security guarantee so outputs remain tensor-product with excluded devices. Construction uses a small constant number of noncommunicating devices (4 grouped, effectively 8 total), composes iteratively, and accumulates only exponentially shrinking error.
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chapters (15)
- 0:00Intro
- 0:34Randomness expansion protocols
- 2:26An expanding list of randomness
- 5:07First attempt
- 6:33Second attempt
- 9:54Input Security
- 11:01Are there Input Secure protocols?
- 11:56Our Input Secure protocol
- 12:55Rigidity of CHSH games
- 13:49Multigame CHSH Rigidity
- 15:04How to launder randomness
- 15:59Not so fast...
- 19:32Final protocol
- 21:44Equivalence Lemma
- 23:08Open Questions
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