Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely nonclassical phenomenon provides a necessary ingredient in many quantum information tasks such as violating a Bell inequality or nonlocally steering part of an entangled state. In this Letter, we characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability. This refers to the temporal freedom a user has in issuing programs to a quantum device. For devices with a classical control and classical output, measurement incompatibility emerges as the essential quantum resource embodied in their functioning. Based on the processing of programmable measurement devices, we construct a quantum resource theory of incompatibility. A complete set of convertibility conditions for programmable devices is derived based on quantum state discrimination with postmeasurement information.

中文翻译：

---

完整的量子不相容性资源理论作为量子可编程性

测量不相容性描述了两个或多个量子测量，它们在给定系统上的预期联合结果无法定义。这种纯粹的非经典现象在许多量子信息任务中提供了必要的成分，例如违反贝尔不等式或纠缠态的非局部操纵部分。在这封信中，我们用可编程测量设备和量子可编程性的一般概念来描述不兼容。这是指用户在向量子设备发布程序时拥有的时间自由。对于具有经典控制和经典输出的设备，测量不兼容会出现在其功能中，成为必不可少的量子资源。在对可编程测量设备进行处理的基础上，我们构建了不相容的量子资源理论。