About the Nature of Quantum Information

Nature, 2000

This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics.

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Some basic facts about QM systems . . . . . . . . . . . . . . . . . . . . . . 2 3 The partial trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Classical Shannon entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 Sundry formulas for the Shannon entropy . . . . . . . . . . . . . . . . . . . 4 6 Von Neumann Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 Sundry formulas for the Von Neumann entropy . . . . . . . . . . . . . . . . 5 8 H(A) versus S(A)? What is dierent? . . . . . . . . . . . . . . . . . . . . 6 9 Case I (Classical) Independent qubits . . . . . . . . . . . . . . . . . . . . . 6 10 Case II (Classical) Correlated qubits . . . . . . . . . . . . . . . . . . . . . 7 11 Case III (Nonclassical--Purely Quantum Mechanical) Entangled (superc

Entropy, 2016

The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics.

Entropy

The new era of quantum foundations, fed by the quantum information theory experience and opened in the early 2000s by a series of memorable papers [...]

2001

Abstract Quantum information theory provides a foundation for such topics as quantum cryptography, quantum error-correction and quantum teleportation. This paper seeks to provide an introduction to quantum information theory for non-physicists at an undergraduate level. It covers basic concepts in quantum mechanics as well as in information theory, and proceeds to explore some results such as Von Neumann entropy, Schumacher coding and quantum error-correction.

Foundations of Physics, 2005

Quantum–mechanical systems may be understood in terms of information. When they interact, they modify the information they carry or represent in two, and only two, ways: by selecting a part of the initial amount of (potential) information and by sharing information with other systems. As a consequence, quantum systems are informationally shielded. These features are shown to be general features of nature. In particular, it is shown that matter arises from quantum–mechanical processes through the constitution of larger ensembles that share some information while living organisms make use of a special form of information selection.

Lecture Notes of the Advanced School, 2014

A brief introduction to quantum information theory in the context of quantum optics is presented. After presenting the fundamental theoretical basis of the subject, experimental * Lecture given at the \Advanced School on Quantum Foundations and Open Quantum Systems" held in

2021

Quantum information science investigates the limits and capabilities of communication, computation, and measurement. In the past two decades, the emergence of new technologies that work close to these limits has begun to transform both science and technology. I will describe how the developments at the frontier of quantum information science promise to enable new approaches to chemistry and materials science, new methods of measuring questions of interest for an improved understanding of our universe, and open the possibility of vast new industries. At the same time, I will consider the tremendous challenges ahead, in both realizing a society that can create these new technologies and in engineering the complex systems necessary to enable vast new industries.

Foundations of Physics, 2018