SciPost Submission Page
Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states
by Márton Mestyán, Balázs Pozsgay, Ian M. Wanless
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Balázs Pozsgay |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202308_00029v3 (pdf) |
| Date accepted: | 2023-12-20 |
| Date submitted: | 2023-12-14 15:34 |
| Submitted by: | Pozsgay, Balázs |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
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''.
Author comments upon resubmission
List of changes
Eqs. (3.1), (3.2) and below (5.7) are fine now.
Published as SciPost Phys. 16, 010 (2024)