  Decoy-state quantum key distribution (QKD) has convincingly been shown the
core solution to secure key exchange. While standard BB84 protocol needs to
prepare and measure all states of two complementary bases, which seriously
restricts its real life applications in photonic integration and high speed
system. Fortunately, a simplified BB84, only sending and receiving three
states, achieves the same asymptotic secret key rate compared with standard
BB84 under coherent attacks. In this work, by skillfully exploiting uncertainty
relation for smooth entropies, we provide the finite-key security bounds for
decoy-state simplified BB84 QKD against coherent attacks in the universally
composable framework. Simulation results show that it can also achieve almost
the same performance compared with standard BB84 even the total number of
pulses is as low as $10^{8}$. We conclude that simplified BB84 can completely
replace standard BB84 to be the best choice for QKD in most common practical
scenarios.
