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arXiv · 2008.03584

Quantum algorithmic randomness

Tejas Bhojraj
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Abstract

Quantum Martin-L\"of randomness (q-MLR) for infinite qubit sequences was introduced by Nies and Scholz. We define a notion of quantum Solovay randomness which is equivalent to q-MLR. The proof of this goes through a purely linear algebraic result about approximating density matrices by subspaces. We then show that random states form a convex set. Martin-L\"of absolute continuity is shown to be a special case of q-MLR. Quantum Schnorr randomness is introduced. A quantum analogue of the law of large numbers is shown to hold for quantum Schnorr random states.

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Tejas Bhojraj. 2020-08-08. Quantum algorithmic randomness. https://doi.org/10.1063/5.0003351

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