Noise and Entropic Uncertainty Relations in Quantum Systems

Abstract

The laws of nature, in the Quantum domain is markedly different from the statistical laws that scientists have developed for classical systems in the field of thermodynamics or information theory. One of the main differences in the quantum domain is the presence of uncertainty relations, which ensures certain properties of a system cannot be fundamentally measured to arbitrary degrees of precision. Entropy is one of the most fundamental properties of quantum systems that gives these kinds of relations called Entropic Uncertainty Relations (EUR). These EURs provide a fundamental tool in the development of many Quantum Computing algorithms such as teleportation. In a world where Quantum Computing looks more and more promising to break the barriers of traditional computing, EUR proves to play a crucial role in developing and strengthening the protocols needed for the paradigm shift. One of the main problems with the use of quantum technologies is that they are rarely robust in the presence of noise, while our immediate operative surroundings have a plethora of noise. So, it becomes increasingly important to study EURs in the presence of noisy channels. In this project we study the development of simple EURs and their behaviour in the presence of noise.