  Standard protocols for quantum key distribution (QKD) require that the sender
be able to transmit in two or more mutually unbiased bases. Here, we analyze
the extent to which the performance of QKD is degraded by diffraction effects
that become relevant for long propagation distances and limited sizes of
apertures. In such a scenario, different states experience different amounts of
diffraction, leading to state-dependent loss and phase acquisition, causing an
increased error rate and security loophole at the receiver. To solve this
problem, we propose a pre-compensation protocol based on pre-shaping the
transverse structure of quantum states. We demonstrate, both theoretically and
experimentally, that when performing QKD over a link with known,
symbol-dependent loss and phase shift, the performance of QKD will be better if
we intentionally increase the loss of certain symbols to make the loss and
phase shift of all states same. Our results show that the pre-compensated
protocol can significantly reduce the error rate induced by state-dependent
diffraction and thereby improve the secure key rate of QKD systems without
sacrificing the security.
