Classical noise in quantum systems.

Abstract

Quantum mechanics contains a fresh and mysterious view of reality. Besides the philosophical intrigue, it has also produced and continues to inspire tantalizing new technological innovations. In any technological system, the designers must contend with the problem of noise. This thesis studies classical noise in two different quantum settings. The first is the classical capacity of a quantum channel with memory. Adding forgetful-memory, attempts to push the boundaries of our understanding of how best to transmit information in the presence of correlated noise. We study the noise within two different frameworks; Algebraic Measure theory and Monte Carlo simulations. Both tools are used to calculate the capacity of the channel as correlations in the noise are increased. The second classical-quantum system investigated is atomic clocks. Using power spectral density methods we study aliasing noise induced by periodic-correction which includes the Dick Effect. We propose a novel multi-window scheme that extends the standard method of noise correction and exhibits better anti-aliasing properties. A uniting thread that emerges is that correlations can be put to good use. In the classical capacity setting, correlations occur between uses of the quantum channel. We show that stronger correlations increase the classical capacity. The benefits of correlation are even seen at a meta-level within the framework of Monte Carlo simulations. Correlations are designed into the algorithm which have nothing to do with real-world correlations, but are abstract correlations created by a Markov chain employed in the algorithm to help efficiently sample from a distribution of exponential size. Finally, in the atomic clock setting, correlations in the measured noise are used to help predict and cancel noise on a short time-scale while trying to limit aliasing. Channel capacity and precise time-keeping are distinct topics and require very different approaches to study. However, common to both topics is their application to com- munication and other tasks, the need to overcome noise and the benefits of exploiting correlations in the noise.