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Jens Eisert
Free University of Berlin

Project Title

Decidable and undecidable in quantum mechanics

Project Summary

Is the number 3571 prime? This is an instance of a decision problem: the answer is either yes or no (here: yes). And even though it may be computationally difficult to come up with a correct answer, one might think that any computer - or mind - should be able to come up with a solution. In seminal work, Alan Turing showed that this is not true: There are decision problems for which no machine and mind can always come to the correct conclusion in finite time. In this proposal, we approach the most fundamental of the physical theories that we know today, quantum mechanics, from the perspective of undecidability. This appears to be a extremely promising arena for research: recent work by us and colleagues shows that there are apparently very simple, natural problems in quantum measurement theory that surprisingly turn out to be undecidable even though the classical analogue is readily decidable. We will develop a new mathematical machinery to investigate undecidability in quantum theory. Apart from a new tool to assess complex quantum systems, our research has potential implications for our world view based on the theory of quantum mechanics and our concept of reality.

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