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<p>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 internal compatibility. In the case of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {M}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">M</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, we discuss a geometric behaviour of the internal compatibility.</p>

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Coexistence of Hilbert space effects and orthogonality

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Anil Kumar Karn

摘要

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 internal compatibility. In the case of \(\mathbb {M}_2\) M 2 , we discuss a geometric behaviour of the internal compatibility.