Quantum key distribution using qudits that each encode one bit of raw key

Abstract

All known qudit-based prepare-and-measure quantum key distribution (PMQKD) 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 PMQKD schemes can be constructed simply by encoding one bit of classical information in each transmitted qudit in the form (|i)±|j))/2, where |i)'s form an orthonormal basis of the 2n-dimensional Hilbert space. Moreover, I prove that these schemes can tolerate up to the theoretical maximum of a 50% BER for n≥2 provided the raw key is generated under a certain technical condition, making them extremely-error-tolerant PMQKD schemes involving the transmission of unentangled finite-dimensional qudits. This shows the potential of processing quantum information using lower-dimensional quantum signals encoded in a higher-dimensional quantum state.