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arXiv:quant-ph/0210005

Quantum information science and complex quantum systems

Michael A. Nielsen

Published Oct 1, 2002• 2 citations
arXivHTMLPDF

Abstract

What makes quantum information science a science? This paper explores the idea that quantum information science may offer a powerful approach to the study of complex quantum systems.
DOI
10.48550/arxiv.quant-ph/0210005

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What makes quantum information science a science? These notes explore the idea that quantum information science may offer a powerful approach to the study of complex quantum systems. We discuss how to quantify complexity in quantum systems, and argue that there are two qualitatively different types of complex quantum system. We also explore ways of understanding complex quantum dynamics by quantifying the strength of a quantum dynamical operation as a physical resource. This is the text for a talk at the ``Sixth International Conference on Quantum Communication, Measurement and Computing'', held at MIT, July 2002. Viewgraphs for the talk may be found at http://www.qinfo.org/talks/.
Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultra-sensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on non-causal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.
We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity. We identify correlations as a central concept connecting quantum information and complex systems science. We present two examples for the power of correlations: using quantum resources to simulate the correlations of a stochastic process and to implement a classically impossible computational task.
Quantum Information is the science that aims to use the unusual behavior of the microscopic world, governed by the laws of Quantum Mechanics, in order to improve the way in which we compute or communicate information. Though the first ideas in this direction come from the early 80’s, it is in the last decade when Quantum Information has suffered an spectacular development. It is impossible to resume in a paper like this one the importance and complexity of the field. Therefore, I will limit to briefly explain some of the initial ideas (considered classical by now), and to briefly suggest some of the modern lines of research. By the nature of this exposition, I have decided to avoid rigor and to concentrate more in ideas and intuitions. Anyhow, I have tried to provide with enough references, in such a way that an interested reader could find there proper theorems and proofs.
Quantum information science is an area of study based on the idea that information science depends on quantum effects in physics. It includes theoretical issues in computational models as well as more experimental topics in quantum physics including what can and cannot be done with quantum information. Subfields include: Quantum computing, Quantum error correction, Quantum complexity theory, Quantum cryptography and its generalization, quantum communication, Quantum communication complexity, Quantum entanglement, Quantum dense coding, Quantum teleportation. In the present book, fifteen typical literatures about Quantum Communication published on international authoritative journals were selected to introduce the worldwide newest progress, which contains reviews or original researches on Communication, mechanics, optics, ect. We hope this book can demonstrate advances in Quantum Communication as well as give references to the researchers, students and other related people.