Quantum distribution functions for radial observables

基于自适应非局域可观测量的量子神经网络准极分解

Quasi-polar Decomposition of Quantum Neural Networks via Adaptive Non-local Observables

该研究采用对角自适应非局域可观测量（DANO）对量子神经网络进行准极分解，将训练转化为谱与李代数空间的轨迹，实验证实其径向谱及角坐标分量与分类准确率相关，为表征量子模型行为提供了新视角。

Wigner Distributions and the Joint Measurement of Incompatible Observables

A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained information. A method is studied for calculating a Wigner distribution from the joint probability distribution obtained in a joint measurement.

黑洞径向几何来自量子自旋链

Black hole radial geometry from a quantum spin chain

本文通过精确可解自旋链编码反德西特黑膜中标量场径向方程，揭示径向坐标即晶格准动量，并在超导处理器上验证，低能下得到共形场论。

Quantum Joint Distributions

In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of desirable properties: they agree with the standard quantum mechanical ones if the observables commute, they also depend continuously on the observables, and under unitary transformations they behave in a reasonable manner.

Distribution of Standard deviation of an observable among superposed states

The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a…

Weak values of a quantum observable and the cross-Wigner distribution

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future.