Heisenberg's uncertainty principle has been understood to set a limitation on measurements, whereas the long standing mathematical formulation does not allow such an interpretation. Recently, a new relation was found by the present author to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing. Here, we discuss the state-dependent notion of precise measurements of a given observable, and consider a perfect distance such that zero distance implies the perfect correlation. Then, we shall show that even in the perfect error notions both the position measuring noise and the momentum disturbance can be arbitrarily small. We also show that it is possible to generalize the new noise-disturbance uncertainty relation to perfect error distances.

Date Published: 12 May 2006
PDF: 9 pages
Proc. SPIE 6244, Quantum Information and Computation IV, 62440Q (12 May 2006); doi: 10.1117/12.667565

Published in SPIE Proceedings Vol. 6244:
Quantum Information and Computation IV
Eric J. Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)