论文标题
可通过量子测量值实现的联合可测量性结构：通过边缘手术不兼容
Joint measurability structures realizable with qubit measurements: incompatibility via marginal surgery
论文作者
论文摘要
量子理论中的测量表现出不相容性，即可能无法共同测量。表示一组测量之间（IN）兼容关系关系的直观方法是通过代表其关节测量性结构的超图：其顶点代表兼容测量的（全部和唯一）子集的测量值。量子理论中的投影测量结果实现了（全部和唯一的）关节可测量性结构。另一方面，由正操作员值衡量标准（POVM）表示的一般测量值可以实现任意的联合可测量性结构。在这里，我们探讨了可以用量子poVM实现的联合可测量性结构的范围。我们开发了一种技术，我们将边缘手术定为条件，以获得从一组兼容测量开始的非平凡的关节可测量性结构。我们在一组特殊的Qubit POVM上展示了边际手术的明确例子，用于构建联合可测量性结构，例如$ n $ cycle和$ n $ specker场景，用于任何整数$ n \ geq 3 $。我们还以$ n \ in \ {4,5,6 \} $ VERTICES显示了各种连接性可测量性结构的可靠性。特别是，我们表明所有可能的连接性可测量性结构具有$ n = 4 $的顶点都是可实现的。我们猜想所有连接性可测量性结构都可以通过量子poVM实现。这与R. Kunjwal等人的无限维度形成对比。 Rev. A 89，052126（2014）。我们的结果还可以根据所需的希尔伯特空间维度最大程度地效率。我们还获得了足够的条件，可以为任何一组二元量子量POVM的联合测量性提供了足够的措施，该二进制量子量POVM为我们的许多结果提供动力，并且应该具有独立的关注。
Measurements in quantum theory exhibit incompatibility, i.e., they can fail to be jointly measurable. An intuitive way to represent the (in)compatibility relations among a set of measurements is via a hypergraph representing their joint measurability structure: its vertices represent measurements and its hyperedges represent (all and only) subsets of compatible measurements. Projective measurements in quantum theory realize (all and only) joint measurability structures that are graphs. On the other hand, general measurements represented by positive operator-valued measures (POVMs) can realize arbitrary joint measurability structures. Here we explore the scope of joint measurability structures realizable with qubit POVMs. We develop a technique that we term marginal surgery to obtain nontrivial joint measurability structures starting from a set of compatible measurements. We show explicit examples of marginal surgery on a special set of qubit POVMs to construct joint measurability structures such as $N$-cycle and $N$-Specker scenarios for any integer $N\geq 3$. We also show the realizability of various joint measurability structures with $N\in\{4,5,6\}$ vertices. In particular, we show that all possible joint measurability structures with $N=4$ vertices are realizable. We conjecture that all joint measurability structures are realizable with qubit POVMs. This contrasts with the unbounded dimension required in R. Kunjwal et al., Phys. Rev. A 89, 052126 (2014). Our results also render this previous construction maximally efficient in terms of the required Hilbert space dimension. We also obtain a sufficient condition for the joint measurability of any set of binary qubit POVMs which powers many of our results and should be of independent interest.
