Mutually unbiased bases for quantum states defined over p-adic numbers
Abstract
We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Qp, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Qp). We find that for every prime p>2 there are at least p+1 MUBs, which is in contrast with the situation for quantum states defined over the real line R for which only 3 MUBs are known. We comment on the possible reason for the difference regarding MUBs between these two infinite dimensional Hilbert spaces.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.