2021/09/30 by Bartosz Regula
Computer Science · Mathematics · Physics and Astronomy · #Fidelity #Monotone polygon #Probabilistic logic #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum state #Resource (disambiguation) #State (computer science) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevlett.128.110505
published as Phys. Rev. Lett. 128, 110505 (2022) · 7 pages, 2 figures. Close to published version. Some results and proofs from v1 of this article have been split off into arXiv:2112.11321
openalex created_date 2021/09/27 · arxiv created 2022/03/15 · openalex publication_date 2022/03/18 · arxiv updated 2022/03/22 · openalex updated_date 2026/08/05
The difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking. We develop a general approach to this problem by introducing a new resource monotone that obeys a very strong type of monotonicity: it can rule out all transformations, probabilistic or deterministic, between states in any quantum resource theory. This allows us to place fundamental limitations on state transformations and restrict the advantages that probabilistic protocols can provide over deterministic ones, significantly strengthening previous findings and extending recent no-go theorems. We apply our results to obtain a substantial improvement in bounds for the errors and overheads of probabilistic distillation protocols, directly applicable to tasks such as entanglement or magic state distillation, and computable through convex optimization. In broad classes of resources, we strengthen our results to show that the monotone completely governs probabilistic transformations -- its monotonicity provides a necessary and sufficient condition for state convertibility. This endows the monotone with a direct operational interpretation, as it can exactly quantify the highest fidelity achievable in resource distillation tasks by means of any probabilistic manipulation protocol.