Entanglement witnesses of four-qubit tripartite separable quantum states

A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Comparing to the entanglement of bipartite quantum systems, less progresses have been made for the entanglement of multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, it is proved that the necessary conditions of tripartite separability are also sufficient at W state side.

Cryogenic Deformation Behavior and Microstructural Characteristics of 2195 Alloy

Cryogenic deformation can improve the strength and plasticity of Al–Li alloy, although the underlying mechanism is still not yet well understood. The effects of cryogenic temperature on the tensile properties and microstructure of an Al–Cu–Li alloy were investigated by means of tensile property test, roughness measurement, scanning electron microscope (SEM), optical microscope (OM), electron backscatter diffraction (EBSD), and transmission electron microscope (TEM). The results indicated that the strength and elongation of the as-annealed (O-state) and solution-treated (W-state) alloys increased with the decrease in deformation temperature, where the increasing trend of elongation of the W-state alloy was more significant than that of the O-state alloy. In addition, a temperature range was observed at approximately 178 K that caused the strength of the W-state alloy to slightly decrease. The decrease in temperature inhibited the dynamic recovery of the Al–Cu–Li alloy, which increased the dislocation density and the degree of work hardening, thus improving the strength of the alloy. At cryogenic temperatures, the internal grain structure was more involved in the deformation and the overall deformation was more uniform, which caused the alloy to have higher plasticity. This study provides a theoretical basis for the cryogenic forming of Al–Li alloy.

Tri-partite entanglement in neutrino oscillations

We investigate and quantify bipartite and tripartite entanglement measures in two- and three-flavor neutrino oscillations. The bipartite entanglement is analogous to the entanglement swapping resulting from a beam splitter in quantum optics. We calculate various entanglement measures, such as the concurrence, negativity, and three-tangle for the three-neutrino system. The significant result is that a monogamy inequality in terms of negativity leads to a residual entanglement, implying genuine tripartite entanglement in the three-neutrino system. We establish an analogy of the three-neutrino state with a generalized W-state class in quantum optics.