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Balázs Pozsgay and Ian M. Wanless, Quantum 8, 1339 (2024). Absolutely maximally entangled (AME) states of $k$ qudits (also known as perfect tensors) are quantum states that have maximal entanglement for all possible bipartitions of the sites/parties. We consider the problem of whether such states can be decomposed into a tensor network with a small number of tensors, such that all physical and all auxiliary spaces have the same dimension $D$. We find that certain AME states with $k=6$ can be decomposed into a network with only three 4-leg tensors; we provide concrete solutions for local dimension $D=5$ and higher. Our result implies that certain AME states with six parties can be created with only three two-site unitaries from a product state of three Bell pairs, or equivalently, with six two-site unitaries acting on a product state on six qudits. We also consider the problem for $k=8$, where we find similar tensor network decompositions with six 4-leg tensors.

When an ordinary electrical conductor—such as a metal wire—is connected to a battery, the electrons in the conductor are accelerated by the electric field created by the battery. While moving, electrons frequently collide with impurity atoms or vacancies in the crystal lattice of the wire, and convert part of their motional energy into lattice vibrations. The energy lost in this process is converted into heat that can be felt, for example, by touching an incandescent light bulb.

😗Year 2022


Superconductivity is reported in magic-angle twisted four-layer and five-layer graphene systems. While they find that all magic-angle graphene systems fit into a unified hierarchy of systems that share a set of flat bands in their electronic band structures, they also report that there is a key distinction between magic-angle twisted bilayer graphene and the other family members, related to the difference in the way the electrons move between the layers in a magnetic field.

A ‘cage of cages’ is how scientists have described a new type of porous material, unique in its molecular structure, that could be used to trap carbon dioxide and another, more potent greenhouse gas.

Synthesized in the lab by researchers in the UK and China, the material is made in two steps, with reactions assembling triangular prism building blocks into larger, more symmetrical tetrahedral cages – producing the first molecular structure of its kind, the team claims.

The resulting material, with its abundance of polar molecules, attracts and holds greenhouse gasses such as carbon dioxide (CO2) with strong affinity. It also showed excellent stability in water, which would be critical for its use in capturing carbon in industrial settings, from wet or humid gas streams.