dorsal/arxiv
View SchemaUsing Classical Probability To Guarantee Properties of Infinite Quantum Sequences
| Authors | Sam Gutmann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9506016 |
| URL | https://arxiv.org/abs/quant-ph/9506016 |
| DOI | 10.1103/PhysRevA.52.3560 |
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 $\sigma^x$ 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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"abstract": "We consider the product of infinitely many copies of a spin-$1\\over 2$\nsystem. We construct projection operators on the corresponding nonseparable\nHilbert space which measure whether the outcome of an infinite sequence of\n$\\sigma^x$ measurements has any specified property. In many cases, product\nstates are eigenstates of the projections, and therefore the result of\nmeasuring the property is determined. Thus we obtain a nonprobabilistic quantum\nanalogue to the law of large numbers, the randomness property, and all other\nfamiliar almost-sure theorems of classical probability.",
"arxiv_id": "quant-ph/9506016",
"authors": [
"Sam Gutmann"
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"doi": "10.1103/PhysRevA.52.3560",
"title": "Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences",
"url": "https://arxiv.org/abs/quant-ph/9506016"
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