Mathematical foundations of quantum information: Measurement and foundations

Details Mathematical foundations of quantum information: Measurement and foundations Mathematical foundations of quantum information: Measurement and foundations

2012-01-25

arxiv.org/abs/1201.5334v1

Physics

Quantum Physics

29 pages, Latex, originally published in Sugaku, Volume 61-2, 2009, pp. 113-132 (in Japanese)

Scientific paper

The purpose of this paper is to survey mathematical foundations of quantum information. We present an axiomatic construction of quantum measurement theory based on completely positive map valued measures, a universally valid new formulation, the Ozawa formulation, of the uncertainty principle for error and disturbance in measurements, the Wigner-Araki-Yanase limit of measurements and the accuracy limit of quantum computing based on conservation laws, and quantum interpretation based on quantum set theory.

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