  The uncertainty principle is an important principle in quantum theory. Based
on this principle, it is impossible to predict the measurement outcomes of two
incompatible observables, simultaneously. Uncertainty principle basically is
expressed in terms of the standard deviation of the measured observables. In
quantum information theory, it is shown that the uncertainty principle can be
expressed by Shannon's entropy. The entopic uncertainty lower bound can be
altered by considering a particle as the quantum memory which is correlated
with the measured particle. We assume that the quantum memory is an open
system. We also select the quantum memory from $N$ qubit which interact with
common reservoir. In this work we investigate the effects of the number of
additional qubits in reservoir on entropic uncertainty lower bound. We conclude
that the entropic uncertainty lower bound can be protected from decoherence by
increasing the number of additional qubit in reservoir.
