2011/04/05 by Wim van Dam, Mark Howard
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Combinatorics #Discrete mathematics #Mathematics #Mutually unbiased bases #Pauli exclusion principle #Physics #Prime (order theory) #Prime power #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum entanglement #Quantum mechanics #Stabilizer (aeronautics) #quant-ph
paper · pdf · doi:10.1103/physreva.84.012117
published as Phys. Rev. A 84, 012117 (2011) · 8 pages, 1 figure
arxiv created 2011/04/05 · openalex publication_date 2011/07/26 · arxiv updated 2011/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We examine the existence and structure of particular sets of mutually unbiased bases (MUBs) in bipartite qudit systems. In contrast to well-known power-of-prime MUB constructions, we restrict ourselves to using maximally entangled stabilizer states as MUB vectors. Consequently, these bipartite entangled stabilizer MUBs (BES MUBs) provide no local information, but are sufficient and minimal for decomposing a wide variety of interesting operators including (mixtures of) Jamio\lkowski states, entanglement witnesses, and more. The problem of finding such BES MUBs can be mapped, in a natural way, to that of finding maximum cliques in a family of Cayley graphs. Some relationships with known power-of-prime MUB constructions are discussed, and observables for BES MUBs are given explicitly in terms of Pauli operators.