  Uncertainty principle has a fundamental role in quantum theory. This
principle states that it is not possible to measure two incompatible observers
simultaneously. The uncertainty principle is expressed logically in terms of
standard deviation of the measured observables. In quantum information it has
been shown that the uncertainty principle can be expressed by means of
Shannon's entropy. Entropic uncertainty relation can be improve by consider an
additional particle as the quantum memory. In the presence of quantum memory
the entropic uncertainty relation is called quantum memory assisted entropic
uncertainty relation. In this work we will consider the case in which the
quantum memory moves inside the leaky cavity. We will show that by increasing
the velocity of the quantum memory the entropic uncertainty lower bound
decreased.
