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.

• Received 26 January 2011

DOI:https://doi.org/10.1103/PhysRevA.83.042316