Coexistence of qubit effects
arXiv:0802.4167 · doi:10.1007/s11128-009-0109-x
Abstract
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.
Version 3 gives much improved structure, more elegant approach, simpler form of result, and proof of equivalence with other approaches in the literature; in Quantum Information Processing (2009)
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