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Heisenberg's uncertainty principle, exemplified by the gamma ray thoughtexperiment, suggests that any finite precision measurement disturbs anyobservables noncommuting with the measured observable. Here, it is shown thatthis statement contradicts the limit of the accuracy of measurements underconservation laws originally found by Wigner in 1950s, and should be modifiedto correctly derive the unavoidable noise caused by the conservation lawinduced decoherence. The obtained accuracy limit leads to an interestingconclusion that a widely accepted, but rather naive, physical encoding ofqubits for quantum computing suffers significantly from the decoherence inducedby the angular momentum conservation law.Comment: 4 pages, to appear in the Proceedings of the Seventh International  Conference on Quantum Communication, Measurement and Computin

Universal Uncertainty Principle and Quantum State Control under Conservation Laws