Bound States for Magic State Distillation in FaultTolerant Quantum Computation
Abstract
Magic state distillation is an important primitive in faulttolerant quantum computation. The magic states are pure nonstabilizer states which can be distilled from certain mixed nonstabilizer states via Clifford group operations alone. Because of the GottesmanKnill theorem, mixtures of Pauli eigenstates are not expected to be magic state distillable, but it has been an open question whether all mixed states outside this set may be distilled. In this Letter we show that, when resources are finitely limited, nondistillable states exist outside the stabilizer octahedron. In analogy with the bound entangled states, which arise in entanglement theory, we call such states bound states for magic state distillation.
 Publication:

Physical Review Letters
 Pub Date:
 January 2010
 DOI:
 10.1103/PhysRevLett.104.030503
 arXiv:
 arXiv:0908.0836
 Bibcode:
 2010PhRvL.104c0503C
 Keywords:

 03.67.Pp;
 Quantum error correction and other methods for protection against decoherence;
 Quantum Physics
 EPrint:
 Published version. This paper builds on a theorem proven in "On the Structure of Protocols for Magic State Distillation", arXiv:0908.0838. These two papers jointly form the content of a talk entitled "Neither Magical nor Classical?", which was presented at TQC 2009, Waterloo