12 May 2006 Noise and disturbance in quantum measurements and operations
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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.
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Masanao Ozawa, Masanao Ozawa, "Noise and disturbance in quantum measurements and operations", Proc. SPIE 6244, Quantum Information and Computation IV, 62440Q (12 May 2006); doi: 10.1117/12.667565; https://doi.org/10.1117/12.667565

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