#
Uncertainly Principle for Quantum Instruments and Computing

Masanao Ozawa (Tohoku Univ.)

## Abstract

The notion of quantum instruments is formalized as the statistical equivalence classes of all the possible quantum measurements and mathematically characterized as normalized completely positive map valued measures under naturally acceptable axioms. Generalized uncertainty relations are established to set a precision limit for any instrument given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to a quantitative generalization of the Wigner- Araki-Yanase theorem on the precision limit of measurements under conservation laws.Applying this,the conservation law induced decoherence in quantum logic operations are analyzed to obtain general precision limits for Hadamard, CNOT, Tofolli and Fredkin gates.

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