State Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts

Classicality and connectedness for state property systems and closure spaces

It has been shown that there is a categorical equivalence between the category SPS of state property systems and the category Cl of closure spaces. In this note we prove, using this equivalence between categories, that the concept of connectedness for closure spaces can be used to formulate a decomposition theorem, which allows us to split a state property system into a number of 'pure nonclassical state property systems' and a 'totally classical state property system'.

Connectedness Applied to Closure Spaces and State Property Systems

In earlier work a description of a physical entity is given by means of a state property system and it is proven that any state property system is equivalent to a closure space. In the present paper we investigate the relations between classical properties and connectedness for closure spaces. The main result is a decomposition theorem, which allows us to split a state property system into a number of 'pure nonclassical state property systems' and a 'totally classical state property system'

Quantum nondemolition measurement of a nonclassical state of a massive object

While quantum mechanics exquisitely describes the behavior of microscopic systems, one ongoing challenge is to explore its applicability to systems of larger size and mass. Unfortunately, quantum states of increasingly macroscopic objects are more easily corrupted by unintentional measurements from the classical environment. Additionally, even the intentional measurements from the observer can further perturb the system. In optomechanics, coherent light fields serve as the intermediary between the fragile mechanical states and our inherently classical world by exerting radiation pressure force…

哪种经典性？有限量子逻辑中的关联、单纯形和乘积规则测试

Which Classicality? Incidence, Simplex, and Product-Rule Tests in Finite Quantum Logics

研究有限量子逻辑结构在不同测试下的经典性特征，区分关联、单纯形和算子函数测试，通过集体GHZ联合测量等示例说明，还计算选定片段的状态去极化阈值，表明其是片段和噪声模型属性。

State property systems and orthogonality

The structure of a state property system was introduced to formalize in a complete way the operational content of the Geneva-Brussels approach to the foundations of quantum mechanics, and the category of state property systems was proven to be equivalence to the category of closure spaces. The first axioms of standard quantum axiomatics (state determination and atomisticity) have been shown to be equivalent to the $T_0$ and $T_1$ axioms of closure spaces, and classical properties to correspond to clopen sets, leading to a decomposition theorem into classical and purely nonclassical components …