No invariant perfect qubit codes

• URL: http://arxiv.org/abs/2210.02483v1
• Date: Wed, 5 Oct 2022 18:03:19 GMT
• Title: No invariant perfect qubit codes
• Authors: Refik Mansuroglu and Hanno Sahlmann
• Abstract summary: Perfect tensors describe highly entangled quantum states that have attracted particular attention in the fields of quantum information theory and quantum gravity. In loop quantum gravity, the natural question arises whether SU(2) invariant tensors, which are fundamental ingredients of the basis states of spacetime, can also be perfect.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Perfect tensors describe highly entangled quantum states that have attracted particular attention in the fields of quantum information theory and quantum gravity. In loop quantum gravity, the natural question arises whether SU(2) invariant tensors, which are fundamental ingredients of the basis states of spacetime, can also be perfect. In this work, we present a number of general constraints for the layout of such invariant perfect tensors (IPTs) and further describe a systematic and constructive approach to check the existence of an IPT of given valence. We apply our algorithm to show that no qubit encoding of valence 4 and 6 can be described by an IPT and close a gap to prove a no-go theorem for invariant perfect qubit encodings.

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