No invariant perfect qubit codes
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 6 can be described by an IPT and close a gap to prove a nogo theorem for invariant perfect qubit encodings. We also provide two alternative proofs for the nonexistence of 4valent qubit IPTs which has been shown in [1, 2].
 Publication:

Journal of High Energy Physics
 Pub Date:
 February 2023
 DOI:
 10.1007/JHEP02(2023)062
 arXiv:
 arXiv:2210.02483
 Bibcode:
 2023JHEP...02..062M
 Keywords:

 Holography and Condensed Matter Physics (AdS/CMT);
 GaugeGravity Correspondence;
 Models of Quantum Gravity;
 Quantum Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 17 pages, v2: small changes in the text, version essentially identical to the one published in JHEP