2018/09/30 by Chunhe Xiong, Asutosh Kumar, Minyi Huang +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Coherence (philosophical gambling strategy) #Coherence length #Coherence theory #Computer science #Discrete mathematics #Fidelity #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum state #Statistical physics #Superposition principle #quant-ph
paper · pdf · doi:10.1103/physreva.99.032305
published as Phys. Rev. A 99, 032305 (2019) · 12 pages, major revision, references updated
arxiv created 2019/01/15 · openalex publication_date 2019/03/04 · arxiv updated 2019/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A fundamental task in any physical theory is to quantify a certain physical quantity in a meaningful way. In this paper, we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding resource quantifiers can be used to characterize a large class of resource theories. Under two assumptions, namely, convexity of ``free states'' and closure of free states under ``selective free operations,'' our general framework of resource theory includes quantum resource theories of entanglement, coherence, partial coherence, and superposition. In partial coherence theory, we show that fidelity of partial coherence of a bipartite state is equal to the minimal error probability of a mixed quantum state discrimination task and vice versa, which complements the main result in Xiong and Wu [J. Phys. A: Math. Theor. 51, 414005 (2018)]. We also compute the analytic expression of fidelity of partial coherence for (2,n) bipartite X states. At last, we study the correlated coherence in the framework of partial coherence theory. We show that partial coherence of a bipartite state, with respect to the eigenbasis of a subsystem, is actually a measure of discord-type quantum correlation.