论文标题
以与结果无关的方式量化可观察到的无样性
Quantifying unsharpness of observables in an outcome-independent way
论文作者
论文摘要
最近，论文中讨论了观察到的unshapness（模糊性）的非常美丽的度量。修订版A 104，052227（2021）]。本文定义的度量是通过不确定性构建的，不取决于结果的值。一组可观察到的属性（例如，不兼容，非扰动）不取决于结果的值。因此，上述论文中的方法与上述事实一致，并且能够测量可观察物的内在效果。在这项工作中，我们还以与结果无关的方式量化了观察物的脱节性。但是我们的方法与上述纸的方法不同。在这项工作中，首先，我们构建了两个Luder的基于仪器的Unshapness措施，并提供了这些措施的紧密上限。然后，我们证明了上述措施在一类模糊过程中的单调性（使观测值更加模糊的过程）。这与资源理论框架一致。然后，我们将方法与上述纸的方法联系起来。接下来，我们尝试构建两种与仪器无关的unshpness措施。特别是，我们定义了两种与仪器无关的措施，并提供了这些度量的紧密上限，然后我们得出了这些措施在一类模糊过程中的单调性的条件，并证明了二分法Qubit可观察的单调性。然后，我们表明，对于未知的测量，可以通过实验确定所有这些测量的值。最后，我们介绍了可观测物的清晰度资源理论的思想。
Recently, a very beautiful measure of the unsharpness (fuzziness) of the observables is discussed in the paper [Phys. Rev. A 104, 052227 (2021)]. The measure which is defined in this paper is constructed via uncertainty and does not depend on the values of the outcomes. There exist several properties of a set of observables (e.g., incompatibility, non-disturbance) that do not depend on the values of the outcomes. Therefore, the approach in the above-said paper is consistent with the above-mentioned fact and is able to measure the intrinsic unsharpness of the observables. In this work, we also quantify the unsharpness of observables in an outcome-independent way. But our approach is different than the approach of the above-said paper. In this work, at first, we construct two Luder's instrument-based unsharpness measures and provide the tight upper bounds of those measures. Then we prove the monotonicity of the above-said measures under a class of fuzzifying processes (processes that make the observables more fuzzy). This is consistent with the resource-theoretic framework. Then we relate our approach to the approach of the above-said paper. Next, we try to construct two instrument-independent unsharpness measures. In particular, we define two instrument-independent unsharpness measures and provide the tight upper bounds of those measures and then we derive the condition for the monotonicity of those measures under a class of fuzzifying processes and prove the monotonicity for dichotomic qubit observables. Then we show that for an unknown measurement, the values of all of these measures can be determined experimentally. Finally, we present the idea of the resource theory of the sharpness of the observables.
