Quantum Key Distribution Using Qudits Each Encoding One Bit Of Raw Key

Abstract: 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.