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arXiv · 1404.6255

Towards Quantifying Complexity with Quantum Mechanics

Ryan Tan·Daniel R. Terno·Jayne Thompson·Vlatko Vedral·Mile Gu
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Abstract

While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified by the complexity of its simplest mathematical model - the model that requires the least past information for optimal future prediction. Here we review how such models, known as $\epsilon$-machines can be further simplified through quantum logic, and explore the resulting consequences for understanding complexity. In particular, we propose a new measure of complexity based on quantum $\epsilon$-machines. We apply this to a simple system undergoing constant thermalization. The resulting quantum measure of complexity aligns more closely with our intuition of how complexity should behave.

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Ryan Tan, Daniel R. Terno, Jayne Thompson, Vlatko Vedral, Mile Gu. 2014-04-24. Towards Quantifying Complexity with Quantum Mechanics. https://doi.org/10.1140/epjp/i2014-14191-2

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