Conservation Laws, Uncertainty Relations, and Quantum Limits of Measurements

The uncertainty relation between the noise operator and the conserved quantity leads to a bound on the accuracy of general measurements. The bound extends the assertion by Wigner, Araki, and Yanase that conservation laws limit the accuracy of “repeatable,” or “nondisturbing,” measurements to general measurements, and improves the one previously obtained by Yanase for spin measurements. The bound represents an obstacle to making a small quantum computer.