  High-dimensional quantum key distribution (QKD) offers secure communication,
with secure key rates that surpass those achievable by QKD protocols utilizing
two-dimensional encoding. However, existing high-dimensional QKD protocols
require additional experimental resources, such as multiport interferometers
and multiple detectors, thus raising the cost of practical high-dimensional
systems and limiting their use. Here, we present and analyze a novel protocol
for arbitrary-dimensional QKD, that requires only the hardware of a standard
two-dimensional system. We provide security proofs against individual attacks
and coherent attacks, setting an upper and lower bound on the secure key rates.
Then, we test the new high-dimensional protocol in a standard two-dimensional
QKD system over a 40 km fiber link. The new protocol yields a two-fold
enhancement of the secure key rate compared to the standard two-dimensional
coherent one-way protocol, without introducing any hardware modifications to
the system. This work, therefore, holds great potential to enhance the
performance of already deployed time-bin QKD systems through a software update
alone. Furthermore, its applications extend across different encoding schemes
of QKD qudits.
