10,883 research outputs found
Coexistence of qubit effects
Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of selfadjoint operators in a two-dimensional complex Hilbert space
On the Sharpness and Bias of Quantum Effects
The question of quantifying the sharpness (or unsharpness) of a quantum
mechanical effect is investigated. Apart from sharpness, another property,
bias, is found to be relevant for the joint measurability or coexistence of two
effects. Measures of bias will be defined and examples given.Comment: Substantially expanded version, with new results and some proofs
correcte
Quantum Mechanics as a Framework for Dealing with Uncertainty
Quantum uncertainty is described here in two guises: indeterminacy with its
concomitant indeterminism of measurement outcomes, and fuzziness, or
unsharpness. Both features were long seen as obstructions of experimental
possibilities that were available in the realm of classical physics. The birth
of quantum information science was due to the realization that such
obstructions can be turned into powerful resources. Here we review how the
utilization of quantum fuzziness makes room for a notion of approximate joint
measurement of noncommuting observables. We also show how from a classical
perspective quantum uncertainty is due to a limitation of measurability
reflected in a fuzzy event structure -- all quantum events are fundamentally
unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku
2009
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