  Dynamical decoupling (DD) is a technique for preserving the coherence of
quantum mechanical states in the presence of a noisy environment. It uses
sequences of inversion pulses to suppress the environmental perturbations by
periodically refocusing them. It has been shown that different sequences of
inversion pulses show vastly different performance, in particular also
concerning the correction of experimental pulse imperfections. Here, we
investigate specifically the role of time-reversal symmetry in the
building-blocks of the pulse sequence. We show that using time symmetric
building blocks often improves the performance of the sequence compared to
sequences formed by time asymmetric building blocks. Using quantum state
tomography of the echoes generated by the sequences, we analyze the mechanisms
that lead to loss of fidelity and show how they can be compensated by suitable
concatenation of symmetry-related blocks of decoupling pulses.
