  The quantum speed limit provides fundamental bound on how fast a quantum
system can evolve between the initial and the final states. For the unitary
evolution, the celebrated Mandelstam-Tamm (MT) bound has been widely studied
for various systems. Here, we prove a stronger quantum speed limit (SQSL) for
all quantum systems undergoing arbitrary unitary evolution and show that the MT
bound is a special case of the stronger quantum speed limit. We apply our
result for single system as well as for composite systems in separable and
entangled states and show that the new bound is indeed tight. The stronger
quantum speed limit will have wide range of applications in quantum control,
quantum computing and quantum information processing.
