论文标题
子空间中的量子测量不相容性
Quantum measurement incompatibility in subspaces
论文作者
论文摘要
我们考虑表征高维量子测量值不兼容的问题。我们介绍了子空间中测量不兼容的概念。也就是说，从一组不兼容的测量值开始，人们考虑了通过投影到任何严格的固定尺寸子空间获得的测量集。我们在子空间中确定了三种可能的不相容性：（i）不可压缩的不兼容：在每个子空间中都变得兼容的测量值，（ii）完全可压缩的不兼容性：在每个子空间中保持不相容的测量，以及（iii）部分可压缩的既不兼容性：在某些sperpace和在某些中不适合在某些中兼容的测量。对于每个课程，我们讨论明确的示例。最后，我们提出了这些想法的一些应用。首先，我们表明，在最简单的Qubit系统中，联合可测量性和共存是两个不兼容的不相等概念。其次，我们强调了结果对量子转向测试的含义。
We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility: measurements that are compatible in some subspace and incompatible in another. For each class we discuss explicit examples. Finally, we present some applications of these ideas. First we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second we highlight the implications of our results for tests of quantum steering.
