Martin-Löf random quantum states

Martin-Löf random quantum states

We extend the key notion of Martin-Löf randomness for infinite bit sequences to the quantum setting, where the sequences become states of an infinite dimensional system. We prove that our definition naturally extends the classical case. In analogy with the Levin-Schnorr theorem, we work toward chara...

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Veröffentlicht in:Journal of mathematical physics 2019-09, Vol.60 (9)
Hauptverfasser: Nies, André, Scholz, Volkher B.
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Sprache:eng
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Incompressibility
Physics
Randomness
Sequences
Turing machines
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description We extend the key notion of Martin-Löf randomness for infinite bit sequences to the quantum setting, where the sequences become states of an infinite dimensional system. We prove that our definition naturally extends the classical case. In analogy with the Levin-Schnorr theorem, we work toward characterizing quantum ML-randomness of states by incompressibility (in the sense of quantum Turing machines) of all initial segments.
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source AIP Journals Complete; Alma/SFX Local Collection
subjects Incompressibility
Physics
Randomness
Sequences
Turing machines
title Martin-Löf random quantum states
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