Quantum Kolmogorov Complexity and Bounded Quantum Memory

TL;DR

This paper investigates how limited quantum memory affects information processing in a simple protocol, revealing new insights into quantum complexity and an extended uncertainty principle involving quantum memory.

Contribution

It introduces a novel analysis of bounded quantum memory effects using quantum Kolmogorov complexity and generalizes the uncertainty principle with quantum memory considerations.

Findings

Bounded quantum memory impacts information estimation in protocols.

A generalized uncertainty principle with quantum memory is derived.

The results highlight the significance of quantum memory limitations in quantum information.

Abstract

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.