More quantum strangeness

Many people who study Mathematics or Computer Science in college often learn about Gödel's First Incompleteness Theorem. This essentially says that any axiomatic system will always be incomplete, because there will always be things that are true that you can't prove from the axioms. This also means that if you keep adding axioms to your system, you'll eventually be able to find propositions that are logically independent from your axioms, so that they can't be either proven or disproven from the axioms. Such logically independent propositions are called "undecidable." Ever since Gödel proved his First Incompleteness Theorem in 1931, the concepts of logical independence and undecidability have been confusing students of mathematics and computer science. They may also start confusing students of physics soon.

Last year, a group of physicists suggested that there's a link between undecidability and randomness. In particular, they show that quantum systems can encode axioms, and that measurements of such systems can tell whether or not logical propositions are decidable or not within the axioms. This means that undecidability can limit what you can learn from physical measurements. They then argue that quantum randomness is really just a physical manifestation of undecidability. Could there be implications of this connection in quantum computing or quantum cryptography?

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