Negative Quasi-Probability Representation is a Necessary Resource for Magic State Distillation

Details Negative Quasi-Probability Representation is a Necessary Resource for Magic State Distillation Negative Quasi-Probability Representation is a Necessary Resource for Magic State Distillation

2012-01-05

arxiv.org/abs/1201.1256v3

Physics

Quantum Physics

5 pages v3: previous version had two copies of the paper displaying

Scientific paper

The magic state model of quantum computation gives a recipe for universal quantum computation using perfect Clifford operations and repeat preparations of a noisy ancilla state. It is an open problem to determine which ancilla states enable universal quantum computation in this model. Here we show that for systems of odd dimension a necessary condition for a state to enable universal quantum computation is that it have negative representation in a particular quasi-probability representation which is a discrete analogue to the Wigner function. This condition implies the existence of a large class of bound states for magic state distillation: states which cannot be prepared using Clifford operations but do not enable universal quantum computation. This condition also enables an efficient experimental test for distillability.

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