2016/12/31 by Alexander Streltsov, Hermann Kampermann, Sabine Wölk +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Coherence (philosophical gambling strategy) #Coherence length #Coherence theory #Coherent states #Computer science #Density matrix #Diagonal #Law #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum entanglement #Quantum mechanics #Resource (disambiguation) #Resource dependence theory #State (computer science) #Statistical physics #Theoretical physics #Unitary state #quant-ph
paper · pdf · doi:10.1088/1367-2630/aac484
published as New J. Phys. 20, 053058 (2018) · 8+3 pages, 2 figures, published version
openalex publication_date 2018/05/14 · arxiv created 2018/06/04 · arxiv updated 2018/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.