  Future quantum technologies rely heavily on good protection of quantum
entanglement against environment-induced decoherence. A recent study showed
that an extension of Uhrig's dynamical decoupling (UDD) sequence can (in
theory) lock an arbitrary but known two-qubit entangled state to the $N$th
order using a sequence of $N$ control pulses [Mukhtar et al., Phys. Rev. A 81,
012331 (2010)]. By nesting three layers of explicitly constructed UDD
sequences, here we first consider the protection of unknown two-qubit states as
superposition of two known basis states, without making assumptions of the
system-environment coupling. It is found that the obtained decoherence
suppression can be highly sensitive to the ordering of the three UDD layers and
can be remarkably effective with the correct ordering. The detailed theoretical
results are useful for general understanding of the nature of controlled
quantum dynamics under nested UDD. As an extension of our three-layer UDD, it
is finally pointed out that a completely unknown two-qubit state can be
protected by nesting four layers of UDD sequences. This work indicates that
when UDD is applicable (e.g., when environment has a sharp frequency cut-off
and when control pulses can be taken as instantaneous pulses), dynamical
decoupling using nested UDD sequences is a powerful approach for entanglement
protection.
