Quantum Kolmogorov Complexity and Bounded Quantum Memory

In this study, the effect of bounded quantum memory in a primitive information protocol has been examined using the quantum Kolmogorov complexity as a measure of information. We employed a toy two-party protocol in which Bob by using a bounded quantum memory and an unbounded classical memory estimates a message that was encoded in qubits by Alice in one of the bases X or Z. Our theorem gave a nontrivial effect of the memory boundedness. In addition, a generalization of the uncertainty principle in the presence of quantum memory has been obtained.