Coexistence of Hilbert space effects and orthogonality
Abstract
In this paper, we show that every pair of absolutely compatible Hilbert space effects are coexistent and exhibit a partial orthogonality property. We introduce the notion of partially ortho-coexistence. We generalize absolute compatibility to obtain more examples of partially ortho-coexistent pairs and introduce the notion of generalized compatibility. In the case of M2, we discuss a geometric behaviour of the generalized compatibility.
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