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.Comment: To appear in Physics Letters
