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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.

Quantum-memory-assisted entropic uncertainty relation with moving quantum memory inside a leaky cavity