2017/06/30 by Mehdi Ahmadi, Hoan Bui Dang, Gilad Gour +1 · 49 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Discrete mathematics #Existential quantification #Lemma (botany) #MAGIC (telescope) #Mathematics #Physics #Programming language #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Set (abstract data type) #Theoretical physics #quant-ph
paper · pdf · doi:10.1103/physreva.97.062332
published in Physical Review A 97(6) (American Physical Society) · 10 pages, 3 figures
arxiv created 2018/06/20 · openalex publication_date 2018/06/20 · arxiv updated 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 semidefinite program, 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.