dorsal/arxiv
View SchemaQuantum Theory as Efficient Representation of Probabilistic Information
| Authors | Johann Summhammer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701181 |
| URL | https://arxiv.org/abs/quant-ph/0701181 |
Abstract
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique property that its dispersion becomes invariant of the underlying probabilities, and therefore invariant of the physical parameters. This also extends to the complex square roots, and it remains true under a unitary transformation. This reveals quantum theory as a theory for making predictions which are as accurate as the input information, without any statistical loss. Our analysis also suggests that from the point of view of information a slightly more accurate theory than quantum theory should be possible.
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"abstract": "Quantum experiments yield random data. We show that the most efficient way to\nstore this empirical information by a finite number of bits is by means of the\nvector of square roots of observed relative frequencies. This vector has the\nunique property that its dispersion becomes invariant of the underlying\nprobabilities, and therefore invariant of the physical parameters. This also\nextends to the complex square roots, and it remains true under a unitary\ntransformation. This reveals quantum theory as a theory for making predictions\nwhich are as accurate as the input information, without any statistical loss.\nOur analysis also suggests that from the point of view of information a\nslightly more accurate theory than quantum theory should be possible.",
"arxiv_id": "quant-ph/0701181",
"authors": [
"Johann Summhammer"
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"title": "Quantum Theory as Efficient Representation of Probabilistic Information",
"url": "https://arxiv.org/abs/quant-ph/0701181"
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