  All known qudit-based prepare-and-measure quantum key distribution (PM-QKD)
schemes are more error resilient than their qubit-based counterparts. Their
high error resiliency comes partly from the careful encoding of multiple bits
of signals used to generate the raw key in each transmitted qudit so that the
same eavesdropping attempt causes a higher bit error rate (BER) in the raw key.
Here I show that highly error-tolerant PM-QKD schemes can be constructed simply
by encoding one bit of classical information in each transmitted qudit in the
form $(|i\rangle\pm|j\rangle)/\sqrt{2}$, where $|i\rangle$'s form an
orthonormal basis of the $2^n$-dimensional Hilbert space. Moreover, I prove
that these schemes can tolerate up to the theoretical maximum of 50\% BER for
$n\ge 2$ provided that the raw key is generated under a certain technical
condition, making them the most error-tolerant PM-QKD schemes involving the
transmission of unentangled finite-dimensional qudits to date. This shows the
potential of processing quantum information using lower-dimensional quantum
signals encoded in a higher-dimensional quantum state.

Quantum Physics