论文标题
某些Qudits
Unsharp measurements, joint measurability and classical distributions for some qudits
论文作者
论文摘要
与操作员的联合测量性相关的经典性通过测量结果的有效经典联合概率分布表现出来。对于dimension $ n $的Qudit，其中$ n $是Prime或Prime的功率，我们提出了一种构造Unsharp版本的投影测量运算符的方法，该方法对操作员为其产生经典关节概率分布的一组量子状态的几何描述，并可以共同测量。具体而言，在$ n^2-1 $尺寸的广义BLOCH球体的设置中，我们确定构造的运算符是可以共同测量的，该状态可用于常规多面体中的同心球家族，这代表导致经典概率分布的状态。我们的构建对与互无偏基（MUB）相关的联合测量性与最佳测量策略之间的联系建立了新的观点，并为长期存在MUB的长期存在$ n = 6 $的持续开放问题提出了必要条件。
Classicality associated with joint measurability of operators manifests through a valid classical joint probability distribution on measurement outcomes. For qudits in dimension $n$, where $n$ is prime or power of prime, we present a method to construct unsharp versions of projective measurement operators which results in a geometric description of the set of quantum states for which the operators engender a classical joint probability distribution, and are jointly measurable. Specifically, within the setting of a generalised Bloch sphere in $n^2-1$ dimensions, we establish that the constructed operators are jointly measurable for states given by a family of concentric spheres inscribed within a regular polyhedron, which represents states that lead to classical probability distributions. Our construction establishes a novel perspective on links between joint measurability and optimal measurement strategies associated with Mutually Unbiased Bases (MUBs), and formulates a necessary condition for the long-standing open problem of existence of MUBs in dimension $n=6$.
