Hannover 2016 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 3: Quantum Information: Concepts and Methods I

Q 3.6: Vortrag

Montag, 29. Februar 2016, 12:15–12:30, e214

Measurement uncertainty is larger than preparation uncertainty — •Reinhard F. Werner, Kais Abdelkhalek, David Reeb, and René Schwonnek — Inst. für Theoret. Physik, Leibniz Universität Hannover

Measurement uncertainty is the quantitative expression of the non-existence of a joint measurement of two observables A and B. It relates the minimal errors one incurs in any attempt at approximate joint measurement and, in particular, in successive measurements like Heisenberg's microscope. This is conceptually different from the usual preparation uncertainty which expresses that there are no states in which both observables have a sharp distribution. Nevertheless, as the new result reported here shows, under very general circumstances preparation uncertainty bounds also give a lower bound on measurement uncertainty. We establish a chain of inequalities involving in decreasing order (1) the errors in a joint measurement based on an approximate quantum cloner (2) the lower bounds on measurement uncertainty, when devices are tested with arbitrary input state (3) the same when the tests are of calibration type, i.e., involve only states with known sharp results for the reference observable and (4) preparation uncertainty. For the standard case of position and momentum (and more generally for observables linked by the Fourier transform on an abelian group) all these inequalities are equalities, but we also give examples showing that each of them may be a proper inequality.