Seminar: Prof Andre Nies, University of Auckland

Algorithmically random spin chains
We survey a notion of algorithmic randomness for infinite qubit sequences. 

Abstract image of spinning top with vivid spin overlay

Image: Jack B & Christoph Hautier / Unsplash

Title: Algorithmically random spin chains

Speaker: Professor Andre Nies, Dept of Computer Science, University of Auckland

Abstract: 
In computability theory, a subfield of mathematical logic, one studies randomness properties of infinite sequences of bits via algorithmic tests. The main notion is due to Martin-Loef (1967). Nies and Scholz  (J. Math. Physics, to appear) have proposed an analogous definition for infinite sequences of qubits, which can be seen as spin chains. 

The talk will survey algorithmic randomness in this setting, including robustness results by Bhojraj (UW Madison).  We will also report on work in progress of Nies and Tomamichael connecting this notion to entropy via a quantum version of the Shannon-McMillan-Breiman theorem.

 

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