2007/01/25 by Johann Summhammer, Summhammer, Johann
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Neural Networks and Reservoir Computing #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0701181
5 figures
arxiv created 2007/01/25 · openalex publication_date 2007/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.