Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation

TL;DR

This paper investigates the limitations of magic state distillation in fault-tolerant quantum computing, revealing the existence of non-distillable states outside the stabilizer octahedron, akin to bound entangled states.

Contribution

It introduces the concept of bound states for magic state distillation, showing that some mixed states outside the stabilizer octahedron cannot be distilled with finite resources.

Findings

Non-distillable states exist outside the stabilizer octahedron.

Bound states for magic state distillation are analogous to bound entangled states.

Finite resource limitations lead to the existence of these bound states.

Abstract

Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure non-stabilizer states which can be distilled from certain mixed non-stabilizer states via Clifford group operations alone. Because of the Gottesman-Knill 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, non-distillable 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.