On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes

Simple item page
dc.creatorRoychowdhury, Vwani P.
dc.creatorVatan, Farrokh
dc.date1997-10-09
dc.date.accessioned2026-07-07T06:14:28Z
dc.date.available2026-07-07T06:14:28Z
dc.descriptionWe first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes. Then we present several examples of nonadditive codes. We show that there exist infinitely many non-trivial nonadditive codes with different minimum distances, and high rates. In fact, we show that nonadditive codes that correct t errors can reach the asymptotic rate R=1-2H(2t/n), where H(x) is the binary entropy function. Finally, we introduce the notion of strongly nonadditive codes (i.e., quantum codes with the following property: the trivial code consisting of the entire Hilbert space is the only additive code that is equivalent to any code containing the given code), and provide a construction for an ((11,2,3)) strongly nonadditive code.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/9710031
dc.identifierhttp://arxiv.org/abs/quant-ph/9710031
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93471
dc.subjectQuantum Physics
dc.titleOn the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes
dc.typetext

Files

Collections

arXiv