To understand how entangled states behave under local quantum operations is an open problem in quantuminformation theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided.
The nonlocality of quantum states on a bipartite system is tested by comparing probabilistic outcomes of two local observables of different subsystems. For a fixed observable A of the subsystem its optimal approximate double A′ of the other system is defined such that the probabilistic outcomes of A′ are almost similar to those of the fixed observable A. The case of σ-finite standard von Neumann algebras is considered and the optimal approximate double A′ of an observable A is explicitly determined. The connection between optimal approximate doubles and quantum correlations is explained. Inspired by quantum states with perfect correlation, like Einstein–Podolsky–Rosen states and Bohm states, the nonlocality power of an observable A for general quantum states is defined as the similarity that the outcomes of A look like the properties of the subsystem corresponding to A′. As an application of optimal approximate doubles, maximal Bell correlation of a pure entangled state on is found explicitly.
Context: Andrographolide (Andro), found in large quantities in Andrographis paniculata Nees (Acanthaceae), is anti-inflammatory, especially in the central nervous system (CNS) glia.Objective: The objective of this study is to test Andro’s ability to reduce allodynia in a spared nerve injury model.Material and methods: Male 30 g BalbC mice were divided into four groups: (1) Sham-operated control (Sham-group); (2) nerve injured and treated with saline (Saline-group); (3) nerve injured and treated with Andro (Andro-group); (4) nerve injured and treated with non-steroidal anti-inflammatory drugs (NSAIDS) (NSAIDS-group). Andro or NSAIDS (diclofenac salt) were injected intraperitoneally at 5 mg/kg body weight daily. Mechanical allodynia was assessed by von Frey tests at 3, 7, and 14 d. For immunohistochemical analysis, samples were collected at 7 d.Results: The threshold for inducing allodynia increased and the response percentage reduced in the Andro-group when compared with the Saline-group, as well as when compared with NSAIDS groups throughout 3–14 d. The ratio of threshold for OP-Andro/OP-saline and for OP-Andro/OP-NSAIDS groups was 20.42 and 11.67 at 14 d, respectively. The ratio of response percentage for OP-Andro/OP-saline and for OP-Andro/OP-NSAIDS was 0.32 and 0.39 at 14 d, respectively. Interleukin-1 (IL-1) immunostaining in the spinal cord was reduced in the Andro-group. Astrocytic activities were not significantly reduced in the Andro-group compared with the Saline-group at 7 d post-operation (PO)Conclusions: Andro reduced mechanical allodynia more than NSAIDS at the same concentration, and the observed behaviour was associated with a reduction in inflammatory cytokine produced in the spinal cord.
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