<p>The Big Bounce model provides an alternative to the classical Big Bang theory. It posits a cyclic universe with phases of contraction and expansion. This raises questions about the preservation of quantum information across these cosmological cycles. In this work, we explore the Quantum Information Theory based on a double Hilbert space framework and a quantum channel. We investigate how information is transferred from the pre-bounce to the post-bounce phase. Analytical and numerical solutions are presented to demonstrate how quantum information, particularly entanglement and coherence, is impacted by different types of quantum noise, such as depolarizing and amplitude damping channels. Our findings suggest that while quantum noise affect information preservation, the use of quantum channels provides a method for analyzing and potentially mitigating information loss.</p>