Algorithm for evaluating distance-based entanglement measures

Quantifying entanglement in quantum systems is an important yet challenging task due to its NP-hard nature.In this work,we propose an efficient algorithm for evaluating distance-based entanglement measures.Our approach builds on Gilbert's algorithm for convex optimization,providing a reliable upper bound on the entanglement of a given arbitrary state.We demonstrate the effectiveness of our algorithm by applying it to various examples,such as calculating the squared Bures metric of entanglement as well as the relative entropy of entanglement for GHZ states,W states,Horodecki states,and chessboard states.These results demonstrate that our algorithm is a versatile and accurate tool that can quickly provide reliable upper bounds for entanglement measures.

Prediction on Phase Stabilities of the Zr-H System from the First-Principles

Basic fundamentals governing the hydrogenation of Zr and its alloys have both theoretical and practical importance.In this work,first-principles calculations have been performed to evaluate the relative stabilities of various possible phases in ZrH_(x)(x=1-2)under different temperatures and pressures.It was predicted that fct-γandεphases with various different H-atom configurations can be energetically favorable for ZrH_(x)(x=1,1.25 and 1.5),while ZrH_(1.75) and ZrH_(2) prefer fct-ε phase only.Fcc-δ phase is less favored in energy at any H concentrations,but can be mechanically stable in some cases.The thermodynamically stable and metastable phase stability diagrams were then constructed for a wide temperature and H concentration range,to predict the environment-dependent formation of ZrH_(x) during hydrogenation.

High-temperature elemental segregation induced structure degradation in high-entropy fluorite oxide

Fluorite-structured oxides constitute an important category of oxides with a wide range of high-temperature applications.Following the concept of high entropy,high-entropy fluorite oxides(HEFOs)have showcased intriguing high-temperature application potential.However,unlocking this potential necessitates an assessment of their long-term stability under high-temperature conditions.In this study,we conducted a prolonged heat treatment at 1000℃on typical HEFO,specifically(CeHfZrGdLa)O_(x).After 100 h,high-intensity X-ray diffraction(XRD)revealed a transition from a single-phase fluorite to a multi-phase configuration.Further investigation by analytical electron microscoy(AEM)demonstrated that this degradation resulted from facilitated element diffusion and consequent escalating chemical fluctuation at high temperatures,leading to spontaneous segregation and separation of Ce and La elements,forming Ce-rich,La-poor,and La-rich phases.Notably,the La-rich phase spontaneously transformed from a fluorite structure(space group Fm3m)to a bixbyite structure(space group Ia3)at elevated temperatures,resulting in the appearance of superstructure reflection in XRD profiles and electron diffraction patterns.Despite the intricate phase decomposition,the energy band gap showed minimal variation,suggesting potential property stability of(CeHfZrGdLa)O_(x)across a broad range of compositions.These findings offer valuable insights into the future applications of HEFOs.