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Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

by Márton Mestyán, Balázs Pozsgay, Ian M. Wanless

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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
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical


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

We are thankful the referees for the renewed review, and especially to referee 1. for checking every detail again. We are honestly sorry for the extra time/work needed. It is not clear what happened, different versions of the tex file got mixed up somehow. In any case, the current version should be fine.

List of changes

Eqs. (3.1), (3.2) and below (5.7) are fine now.

Published as SciPost Phys. 16, 010 (2024)

Reports on this Submission

Anonymous Report 1 on 2023-12-14 (Invited Report)


Thank you for correcting the mistakes. This version is ready for publication.

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