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arXiv:1611.02176 · Reports on Progress in Physics

Randomness in quantum mechanics: philosophy, physics and technology

Manabendra Nath Bera, Antonio Acín, Marek Kuś, Morgan W. Mitchell, Maciej Lewenstein

Published Nov 6, 2017• 111 citations
arXivHTMLPDF

Abstract

This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology. For this reason the article contains three parts that will be essentially devoted to different aspects of quantum randomness, and even directed, although not restricted, to various audiences: a philosophical part, a physical part, and a technological part. For these reasons the article is written on an elementary level, combining simple and non-technical descriptions with a concise review of more advanced results. In this way readers of various provenances will be able to gain while reading the article.

DOI
10.1088/1361-6633/aa8731

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This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology. For this reason the article contains three parts that will be essentially devoted to different aspects of quantum randomness, and even directed, although not restricted, to various audiences: a philosophical part, a physical part, and a technological part. For these reasons the article is written on an elementary level, combining simple and non-technical descriptions with a concise review of more advanced results. In this way readers of various provenances will be able to gain while reading the article.
This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from
This concise and self-contained book opens completely novel areas of research by directly implementing concepts from quantum physics into areas of social science. It constructs compelling arguments originating from fundamental concepts in physics and the philosophy of science, including key developments in economics and finance, then surveys the important work which has been performed to date through applying the formalism of quantum mechanics to decision making and finance. The book is accessible to graduate students and researchers in social science and physics, as well as avid interdisciplinary readers. This title is part of the Flip it Open Programme and may also be available Open Access. Check our website Cambridge Core for details.
Recent tremendous development of quantum information theory has led to a number of quantum technological projects, e.g. quantum random generators. This development had stimulated a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is the elaboration of a consistent and commonly accepted interpretation of a quantum state. Closely related problem is the clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review, we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. We also discuss briefly “digital philosophy”, its role in physics (classical and quantum) and its coupling to the information interpretation of quantum mechanics (QM).
Quantum mechanics allows a remarkably accurate description of nature and powerful predictive capabilities. The analyses of quantum systems and their interpretation lead to many surprises, for example, the ability to detect the characteristics of an object without ever touching it in any way, via "interaction-free measurement," or the teleportation of an atomic state over large distances. The results can become downright bizarre. Quantum mechanics is a subtle subject that usually involves complicated mathematics -- calculus, partial differential equations, etc., for complete understanding. Most texts for general audiences avoid all mathematics. The result is that the reader misses almost all deep understanding of the subject, much of which can be probed with just high-school level algebra and trigonometry. Thus, readers with that level of mathematics can learn so much more about this fundamental science. The book starts with a discussion of the basic physics of waves (an appendix reviews some necessary classical physics concepts) and then introduces the fundamentals of quantum mechanics, including the wave function, superposition, entanglement, Bell's theorem, etc., and applications to Bose--Einstein condensation, quantum computing, and much more. The interpretation of the mathematics of quantum mechanics into a world view has been the subject of much controversy. The result is a variety of conflicting interpretations, from the famous Copenhagen view of Bohr to the multiple universes of Everett. We discuss these interpretations in the chapter "What is a wave function?" and include some very recent advances, for example, quantum Bayesianism, and measurements of the reality of the wave function.
There are several (general) philosophy of physics textbooks on the market.1 An obvious question to ask at the outset then is: Why another one? In his “Some Philosophical Aspects of Particle Physics”, Michael Redhead bemoans the common practice of philosophers of science of dealing with examples “which are no longer of current research interest in science” ((1980), p. 279). This practice is still common even among many philosophers of physics, and, for the most part, the available textbooks continue to engage in this practice. Generally, one finds a little spacetime, a little statistical mechanics, and a little quantum theory. Now, these are of course the ‘pillars’ of modern physics, so it is what we should expect to be covered in any textbook on the philosophy of physics worth its salt (and, indeed, they are well represented in this book). However, the issues that are dealt with are usually very old fashioned and very limited in scope: ‘spacetime’ means ‘the twins paradox’ (and possibly conventionalism); ‘statistical mechanics’ means ‘time asymmetry’; and ‘quantum theory’ means ‘the measurement problem’. Redhead is surely right that this leads physicists to “regard philosophy of science as somewhat irrelevant”. Rightly so, too, if this were in fact representative of much of what actually goes on in philosophy of physics. However, the state of play as represented in philosophy of physics and (some) philosophy of science journals shows a very different level of engagement, with philosophers of physics investigating the frontiers of scientific research. This disparity (or the impression of such) is the raison d’eˆtre for the book you are now reading. The result is an introductory textbook covering those portions of philosophy of physics research that other textbooks fail to cover, or cover only very briefly or very simplistically. The three pillars of modern physics-relativity, quantum theory and statistical mechanics-are still represented, then, but from a more advanced and contemporary perspective.