Blind encoding into qudits

Abstract

We consider the problem of encoding classical information into unknown qudit states belonging to any basis, of a maximal set of mutually unbiased bases, by one party and then decoding by another party who has perfect knowledge of the basis. Working with qudits of prime dimensions, we point out a no-go theorem that forbids shift operations on arbitrary unknown states. We then provide the necessary conditions for reliable encoding/decoding.