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arXiv · 1706.03828

Quantification and manipulation of magic states

Mehdi Ahmadi·Hoan Bui Dang·Gilad Gour·Barry C. Sanders
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Abstract

Magic states can be used as a resource to circumvent the restrictions due to stabilizer-preserving operations, and magic-state conversion has not been studied in the single-copy regime thus far. Here we solve the question of whether a stabilizer-preserving quantum operation exists that can convert between two given magic states in the single-shot regime. We first phrase this question as a feasibility problem for a semi-definite program (SDP), which provides a procedure for constructing a stabilizer-preserving quantum operation (free channel) if it exists. Then we employ a variant of the Farkas Lemma to derive necessary and sufficient conditions for existence, and this method is used to construct a complete set of magic monotones.

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Mehdi Ahmadi, Hoan Bui Dang, Gilad Gour, Barry C. Sanders. 2017-06-12. Quantification and manipulation of magic states. https://doi.org/10.1103/physreva.97.062332

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