Quantum Theory as Efficient Representation of Probabilistic Information

Details Quantum Theory as Efficient Representation of Probabilistic Information Quantum Theory as Efficient Representation of Probabilistic Information

2007-01-25

arxiv.org/abs/quant-ph/0701181v1

Physics

Quantum Physics

5 figures

Scientific paper

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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