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  1. Abstract

    Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states. First, we define the unextendible entanglement, a family of entanglement measures based on the concept of a state-dependent set of free states. The intuition behind these measures is that the more entangled a bipartite state is, the less entangled each of its individual systems is with a third party. Second, we demonstrate that the unextendible entanglement is an entanglement monotone under two-extendible quantum operations, including local operations and one-way classical communication as a special case. Normalization and faithfulness are two other desirable properties of unextendible entanglement, which we establish here. We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation.

     
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  2. Free, publicly-accessible full text available January 24, 2025
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  6. Integrating multidisciplinary efforts from physics, chemistry, biology, and materials science, the field of single-molecule electronics has witnessed remarkable progress over the past two decades thanks to the development of single-molecule junction techniques. To date, researchers have interrogated charge transport across a broad spectrum of single molecules. While the electrical properties of covalently linked molecules have been extensively investigated, the impact of non-covalent interactions has only started to garner increasing attention in recent years. Undoubtedly, a deep understanding of both covalent and non-covalent interactions is imperative to expand the functionality and scalability of molecular-scale devices with the potential of using molecules as active components in various applications. In this review, we survey recent advances in probing how non-covalent interactions affect electron transmission through single molecules using single-molecule junction techniques. We concentrate on understanding the role of several key non-covalent interactions, including π–π and σ–σ stacking, hydrogen bonding, host–guest interactions, charge transfer complexation, and mechanically interlocked molecules. We aim to provide molecular-level insights into the structure–property relations of molecular junctions that feature these interactions from both experimental and theoretical perspectives. 
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  7. Understanding chemical processes at the single-molecule scale represents the ultimate limit of analytical chemistry. Single-molecule detection techniques allow one to reveal the detailed dynamics and kinetics of a chemical reaction with unprecedented accuracy. It has also enabled the discoveries of new reaction pathways or intermediates/transition states that are inaccessible in conventional ensemble experiments, which is critical to elucidating their intrinsic mechanisms. Thanks to the rapid development of single-molecule junction (SMJ) techniques, detecting chemical reactions via monitoring the electrical current through single molecules has received an increasing amount of attention and has witnessed tremendous advances in recent years. Research efforts in this direction have opened a new route for probing chemical and physical processes with single-molecule precision. This review presents detailed advancements in probing single-molecule chemical reactions using SMJ techniques. We specifically highlight recent progress in investigating electric-field-driven reactions, reaction dynamics and kinetics, host–guest interactions, and redox reactions of different molecular systems. Finally, we discuss the potential of single-molecule detection using SMJs across various future applications. 
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  8. Abstract

    SiAlON ceramics are of interest for high‐risk applications such as biomedical implants and combustion engine turbines. This work is part of a larger study aimed at leveraging atomic‐ or molecular‐scale additives to control the densification, microstructures, and ultimate structural properties of SiAlONs. Here, we investigate the effects of boron in silicon nitride‐based ceramics. The present work demonstrates a possible chemical method for controlling the microstructural development of SiAlONs by incorporating boric acid (H3BO3) into the starting powder blend. Raman spectroscopy and11B solid‐state magic angle spinning nuclear magnetic resonance cooperatively indicate that after sintering, boron exists in threefold coordination with nitrogen in the turbostratic boron nitride (t‐BN) structure. The results of this work indicate that the incorporation of boron and generation of t‐BN bonding in the SiAlON system result in a narrower grain size distribution, a suppression of second phases such as yttrium aluminosilicates, and ultimately, increased flexure strength. A separate fractographic study showed that SiAlONs fabricated with 3 wt% boric acid exhibited fracture origins such as subtle surface flaws or cracks, while lower dopant levels and undoped SiAlONs typically failed from flaws such as inclusions or large grains. It is argued that the modification of the intergranular glass chemistry and resulting generation of t‐BN reduces atomic diffusion through the grain boundary phase and inhibits the crystallization of second phases as well as exaggerated grain growth that often characterizes the development of β′‐SiAlON.

     
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  9. The idea of using individual molecules as conducting wires, regulators, and interconnects for charges in electronic circuitry has catalyzed the vibrant development of the field of single-molecule electronics. The ability to reliably and repeatedly construct single-molecule junctions (SMJs) has enabled the study of charge transport through a broad spectrum of individual molecules. Over the past decade, the capability of the SMJ platform has been greatly expanded thanks to the development of new experimental techniques and the integration of knowledge and methodologies from other disciplines. New opportunities beyond electrical conductance have emerged at the atomic and molecular scale. It has been demonstrated in many recent studies that the SMJ can now serve as a powerful and versatile tool to address critical physical and chemical questions that are otherwise inaccessible. This perspective focuses on the new capabilities and functionalities of the SMJ beyond conductance measurements and how they have enabled the investigation of crucial single-molecule processes and advanced our understanding beyond molecular electronics. 
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