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Entanglement Theory Quantum Correlations
Quantum algorithmic randomness
arXiv
Authors: Tejas Bhojraj
Year
2020
Paper ID
21605
Status
Preprint
Abstract Read
~2 min
Abstract Words
91
Citations
N/A
Abstract
Quantum Martin-Löf 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-Löf 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.
Why This Paper Matters
- This paper contributes to the Entanglement Theory & Quantum Correlations research area in the Quantum Articles archive.
- It adds a 2020 reference point for readers tracking recent quantum research.
- Quantum Martin-Löf randomness (q-MLR) for infinite qubit sequences was introduced by Nies and Scholz.
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