  We propose and experimentally demonstrate a new scheme for measuring
high-dimensional phase states using a two-photon interference technique, which
we refer to as quantum-controlled measurement. Using this scheme, we implement
a $d$-dimensional time-phase quantum key distribution (QKD) system and achieve
secret key rates of 5.26 and 8.65 Mbps using $d = 2$ and $d = 8$ quantum
states, respectively, for a 4~dB channel loss, illustrating that
high-dimensional time-phase QKD protocols are advantageous for low-loss quantum
channels. This work paves the way for practical high-dimensional QKD protocols
for metropolitan-scale systems. Furthermore, our results apply equally well for
other high-dimensional protocols, such as those using the spatial
degree-of-freedom with orbital angular momentum states being one example.
