Random sequences of quantum bits
Date/Time:16 Jul 2019 16:00
Venue: S17 #04-06 SR1
Speaker: Andre Nies, University of Auckland
Random sequences of quantum bits
Martin-Loef formalised in 1966 the intuitive notion of randomness of infinite sequences of bits via algorithmic tests. In this talk, we investigate what happens if we replace classical bits by quantum bits.
We first provide a framework to formalise infinite sequences of quantum bits as states of a suitable C* algebra. Thereafter we introduce an analog of Martin-Loef’s notion. We show that for classical bit sequences the two notions coincide. We also discuss quantum Kolmogorov complexity for finite sequences of quantum bits and its relationship to quantum Martin-Loef randomness. Finally, we consider an effective version of the Shannan-McMillan-Breiman theorem in the quantum setting.
This is joint work with Volkher Scholz. The paper is available at http://arxiv.org/abs/1709.08422.
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