TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.1.010
TI  - Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states
PY  - 2024/01/09
UR  - https://scipost.org/SciPostPhys.16.1.010
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 1
SP  - 010
A1  - Mestyán, Márton
AU  - Pozsgay, Balázs
AU  - Wanless, Ian M.
AB  - 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".
ER  -

@Article{10.21468/SciPostPhys.16.1.010,
	title={{Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states}},
	author={Márton Mestyán and Balázs Pozsgay and Ian M. Wanless},
	journal={SciPost Phys.},
	volume={16},
	pages={010},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.1.010},
	url={https://scipost.org/10.21468/SciPostPhys.16.1.010},
}