**A new paradigm for decoding quantum incompatibility** - Huangjun Zhu

The existence of observables that are incompatible or not
jointly measurable is a characteristic feature of quantum mechanics,
which lies at the root of a number of nonclassical phenomena, such as
uncertainty relations, wave--particle dual behavior, Bell-inequality
violation, and contextuality. However, no intuitive criterion is
available for determining the compatibility of even two (generalized)
observables, despite the overarching importance of this problem and
intensive efforts of many researchers. Here we introduce an information
theoretic paradigm together with an intuitive geometric picture for
decoding incompatible observables, starting from two simple ideas: Every
observable can only provide limited information and information is
monotonic under data processing. By virtue of quantum estimation theory,
we introduce a family of universal criteria for detecting incompatible
observables and a natural measure of incompatibility, which are
applicable to arbitrary number of arbitrary observables. Based on this
framework, we derive a family of universal measurement uncertainty
relations, provide a simple information theoretic explanation of
quantitative wave--particle duality, and offer new perspectives for
understanding Bell nonlocality, contextuality, and quantum precision limit.