Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA.
Phys Rev Lett. 2019 Aug 16;123(7):070401. doi: 10.1103/PhysRevLett.123.070401.
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability distributions associated with different quantum measurements can be converted into one another by probabilistic postprocessing. The induced preorder over quantum measurements is directly related to multivariate majorization and gives rise to families of monotones, i.e., scalar quantifiers that preserve the ordering. For the case of orthogonal measurement we establish a quantitative connection between incompatibility, quantum coherence and entropic uncertainty relations. We generalize the construction to include arbitrary positive-operator-valued measurements and report complete families of monotones.
受量子资源理论的启发，我们提出了一种相对于参考基的量子测量的不相容性概念。该概念是通过考虑在该基下对角的态，并研究与不同量子测量相关联的概率分布是否可以通过概率后处理相互转换而产生的。诱导的量子测量的偏序与多元-majorization 直接相关，并产生一族单调函数，即保持排序的标量量化器。对于正交测量的情况，我们在不相容性、量子相干性和熵不确定性关系之间建立了定量联系。我们将构造推广到包括任意正算子值测量，并报告完整的单调函数族。
