No Quantum Ramsey Theorem for Stabilizer Codes

DOI10.1109/TIT.2020.3018024zbMATH Open1473.81053arXiv2004.07884OpenAlexW3100637544MaRDI QIDQ5151720

Travis Russell, Yannis Bousba

Publication date: 22 February 2021

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: In this paper we study the quantum graphs of mixed-unitary channels generated by tensor products of Pauli operators, which we call Pauli channels. We show that most quantum graphs arising from Pauli channels have non-trivial quantum cliques or quantum anticliques which are stabilizer codes. However, a reformulation of Nik Weaver's quantum Ramsey theorem in terms of stabilizer codes and Pauli channels fails. Specifically, for every positive integer $n$, there exists an $n$-qubit Pauli channel for which any non-trivial quantum clique or quantum anticlique fails to be a stabilizer code.

Full work available at URL: https://arxiv.org/abs/2004.07884

zbMATH Keywords

quantum graphsPauli channelsstabilizer codesquantum anti-cliquesquantum cliquesqubit Pauli channel

Mathematics Subject Classification ID

Generalized Ramsey theory (05C55) Computational stability and error-correcting codes for quantum computation and communication processing (81P73)

Related Items (1)

Nonexistence of some quantum jump codes with specified parameters

This page was built for publication: No Quantum Ramsey Theorem for Stabilizer Codes

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5151720)