The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular.

中文翻译：

---

一般概率理论中的操作限制

一般概率理论的形式主义提供了一种通用范式，适用于将包括经典和量子系统在内的各种物理系统描述为特殊情况。与通常的无限制假设相反，给定理论中可访问的仪表集可能因不同原因而受到限制，这就提出了一个问题，即对仪表的哪些限制在操作上是相关的。我们认为必须在模拟下关闭所有操作限制，其中模拟方案涉及仪表的混合和经典后处理。我们将此类操作限制分为三类：源于效果限制的仪表限制；不以任何方式限制效果集的仪表限制；以及所有其他限制。我们充分描述了第一类限制，并讨论了它与凸效应子代数的联系。我们展示了属于第二类的限制可以施加严重的物理限制，尽管所有效果都是可以访问的，例如，通过有效的二分仪对纯量子态进行明确区分。我们进一步证明，存在属于第三类的物理上有意义的限制。所提出的对操作限制的研究提供了对可访问测量如何修改一般概率理论，特别是量子理论的更好理解。我们展示了属于第二类的限制可以施加严重的物理限制，尽管所有效果都是可以访问的，例如，通过有效的二分仪对纯量子态进行明确区分。我们进一步证明，存在属于第三类的物理上有意义的限制。所提出的对操作限制的研究提供了对可访问测量如何修改一般概率理论，特别是量子理论的更好理解。我们展示了属于第二类的限制可以施加严重的物理限制，尽管所有效果都是可以访问的，例如，通过有效的二分仪对纯量子态进行明确区分。我们进一步证明，存在属于第三类的物理上有意义的限制。所提出的对操作限制的研究提供了对可访问测量如何修改一般概率理论，特别是量子理论的更好理解。