Quantification and manipulation of magic states
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.
Cite
@article{arxiv.1706.03828,
title = {Quantification and manipulation of magic states},
author = {Mehdi Ahmadi and Hoan Bui Dang and Gilad Gour and Barry C. Sanders},
journal= {arXiv preprint arXiv:1706.03828},
year = {2018}
}
Comments
10 pages, 3 figures