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Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences

Sam Gutmann
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Abstract

We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $σ^x$ measurements has any specified property. In many cases, product states are eigenstates of the projections, and therefore the result of measuring the property is determined. Thus we obtain a nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability.

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Sam Gutmann. 1995-06-12. Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences. https://doi.org/10.1103/physreva.52.3560

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