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Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states
by M\'arton Mesty\'an, Bal\'azs Pozsgay, Ian M. Wanless
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Submission summary
| Authors (as registered SciPost users): | Balázs Pozsgay |
| Submission information | |
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| Preprint Link: | scipost_202308_00029v2 (pdf) |
| Date submitted: | 2023-12-05 11:13 |
| Submitted by: | Pozsgay, Balázs |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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
Referee 1 had 4 requests. Here are our replies:
1. We added a footnote about the reason, why we introduce both $U$ and $\check U$, at the position where $U$ is introduced.
2. Indeed, these were small typos. Now corrected.
3. Again, a small typo, now corrected.
4. The general derivations of graphs states depend on $N$ being a prime number. We write this in the first paragraph of the Section. We did not want to discuss all the derivations, to make clear what holds and what does not hold if $N$ is prime. So all of the Section focuses on $N$ being prime. We are not sure how to make this more pronounced, so we left this as it is.
Current status:
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Thank you for considering my previous comments. In principal, I am happy with the updated manuscript and proposed changes. However, in this updated version 2, I can see only the added footnote, but the typos in Eqs. 3.1 and 3.2 and after Eq. 5.7 seem to be still present. Please correct them properly. As soon as this is done, the manuscript is ready for publication from my point of view.