# Tradeoffs for reliable quantum information storage in 2D systems

 Titre Tradeoffs for reliable quantum information storage in {2D} systems Type de publication Journal Article Nouvelles publications 2010 Auteurs Bravyi S, Poulin D, Terhal BM Journal Physical Review Letters Volume 104 Pagination 050503 Mots clés Error correction, Self correcting Résumé We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits $k$, the distance of the code $d$, and the number of particles $n$. It is shown that $kd^2=O(n)$ where the coefficient in $O(n)$ depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. The analogous tradeoff for the classical information storage is $k\sqrt{d} =O(n)$.