论文标题
量子测量的熵
Entropy of Quantum Measurements
论文作者
论文摘要
如果$ a $是量子效应，而$ρ$是一个状态，我们将定义$ρ$ -Entropy $ s_a（ρ）$，这给出了$ a $ $ a $提供约$ρ$的不确定性的数量。较小的$ s_a（ρ）$是，$ a $的衡量信息越多。在〜2节中，我们提供$ s_a（ρ）$的界限，并表明如果$ a+b $是效果，则$ s_ {a+b}（ρ）（ρ）\ ge s_a（ρ）+s_b（ρ）$。然后，我们证明了涉及凸的效应混合物的结果。我们还考虑了效果的顺序产品及其$ρ$ - 凝管。在〜3节中，我们使用$ s_a（ρ）$来定义可观察到的$ a $的$ρ$ -Entropy $ s_a（ρ）$。我们表明，$ s_a（ρ）$直接提供$ρ$ -Entropy $ s_ \ iScript（ρ）$，用于乐器$ \ iScript $。我们为$ s_a（ρ）$建立界限，并证明获得这些界限时的特征。这些简化了文献中给出的结果证明。我们还考虑用于测量模型的$ρ$ entropies，可观察物的顺序产物和可观察到的粗粒。提供了说明理论的各种示例。
If $a$ is a quantum effect and $ρ$ is a state, we define the $ρ$-entropy $S_a(ρ)$ which gives the amount of uncertainty that a measurement of $a$ provides about $ρ$. The smaller $S_a(ρ)$ is, the more information a measurement of $a$ gives about $ρ$. In Section~2, we provide bounds on $S_a(ρ)$ and show that if $a+b$ is an effect, then $S_{a+b}(ρ)\ge S_a(ρ)+S_b(ρ)$. We then prove a result concerning convex mixtures of effects. We also consider sequential products of effects and their $ρ$-entropies. In Section~3, we employ $S_a(ρ)$ to define the $ρ$-entropy $S_A(ρ)$ for an observable $A$. We show that $S_A(ρ)$ directly provides the $ρ$-entropy $S_\iscript (ρ)$ for an instrument $\iscript$. We establish bounds for $S_A(ρ)$ and prove characterizations for when these bounds are obtained. These give simplified proofs of results given in the literature. We also consider $ρ$-entropies for measurement models, sequential products of observables and coarse-graining of observables. Various examples that illustrate the theory are provided.
