Quantum Foundations: General Outlook

R. Eisenschitz

Art Hobson

Vlatko Vedral

Abstract This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.

V. P. Karassiov

Martin Ringbauer

Paul Hockett

In this chapter, the three case studies are summarised, compared and contrasted. General conclusions on the state of matrix element retrieval using the generalised bootstrap protocol are made (herein explored up to 38 complex matrix elements or, correspondingly, a 38 x 38 density matrix, in the largest case study). Future routes of exploration for these cases and improvements for the bootstrap methodology beyond those tested herein are discussed, along with an outlook and general perspective on the topic.