Related papers: No quantum Ramsey theorem for stabilizer codes

No quantum Ramsey theorem for stabilizer codes

URL: http://arxiv.org/abs/2004.07884v2
Date: Mon, 17 Aug 2020 18:16:32 GMT
Title: No quantum Ramsey theorem for stabilizer codes
Authors: Yannis Bousba and Travis B. Russell
Abstract summary: We show that most quantum graphs arising from Pauli channels have non-trivial quantum cliques or quantum anticliques which are stabilizer codes. 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.
Score: 3.8073142980733
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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