Noncommutative Martin-Lof randomness : on the concept of a random sequence of qubits
Abstract
Martin-Lof's definition of random sequences of cbits as those not belonging to any set of constructive zero Lebesgue measure is reformulated in the language of Algebraic Probability Theory. The adoption of the Pour-El Richards theory of computability structures on Banach spaces allows us to give a natural noncommutative extension of Martin-Lof's definition, characterizing the random elements of a chain Von Neumann algebra. In the particular case of the minimally informative noncommutative alphabet our definition reduces to the definition of a random sequence of qubits.
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