论文标题
空间对称量子状态的多向单位性和最大纠缠状态
Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states
论文作者
论文摘要
我们认为文献中各个地方都出现了双重统一运算符及其多腿概括。这些对象可以与具有特殊纠缠模式的多方量子状态有关：这些位点以空间对称模式排列，并且这些状态对于从给定几何学的反射对称性的所有两部分都具有最大的纠缠。我们考虑那些与几何对称群相对于状态本身不变的情况。最简单的例子是那些也是自我双重和反射不变的双重统一运算符，但我们也考虑了六边形，立方体和八面体几何形状的概括。我们为这些对象为各种局部维度提供了许多构造和具体示例。我们所有的示例都可以用来在1+1或2+1维度中构建量子蜂窝自动机，并在``时间方向''中具有多个等效的选择。
We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are arranged in a spatially symmetric pattern and the states have maximal entanglement for all bipartitions that follow from the reflection symmetries of the given geometry. We consider those cases where the state itself is invariant with respect to the geometrical symmetry group. The simplest examples are those dual unitary operators which are also self dual and reflection invariant, but we also consider the generalizations in the hexagonal, cubic, and octahedral geometries. We provide a number of constructions and concrete examples for these objects for various local dimensions. All of our examples can be used to build quantum cellular automata in 1+1 or 2+1 dimensions, with multiple equivalent choices for the ``direction of time''.
