“Quantum Chance” (Springer, 2014) by Nicolas Gisin is a slim volume about entanglement, quantum nonlocality, and the Bell experiment. (The book was originally published in French in 2012; this review is of the English translation.) Gisin is well known both for his deep interest in the foundations of quantum mechanics and for his experimental expertise. That expertise has made him a pioneer in the practical development of quantum cryptography; but, combined with his insight into quantum theory, it has also allowed him to devise ingenious tests of quantum mechanical predictions. His long consideration of these questions informs every page of this book, where he presents his arguments in a clear and engaging style.

The book begins by postulating a peculiar telephone. Alice and Bob–the heroes of many a paper on quantum information–each have a telephone, which is useless for communication: it produces only random noise. But they discover that the noise produced on the two sides is perfectly synchronized. Being good scientists, they try to determine whether the correlations arise due to communication from one side to the other, or due to some common cause, such as a long random sequence stored identically in each telephone before they were distributed.

From this science fictional scenario we are led to the idea of a Bell experiment: two widely separated experimenters, each equipped with a black box that has two settings and two possible outputs. Gisin lays out the description of a Bell game (actually, the CHSH game), and derives the CHSH inequality that must be satisfied if the two black boxes cannot communicate, but are correlated due to a common cause. He then describes how such a Bell test can be carried out in an actual quantum experiment, and how quantum mechanics predicts that the inequality is violated. This, in the language commonly used in quantum theory, is *quantum nonlocality*.

From there he presents related concepts from the heart of quantum information: the no-cloning theorem and entanglement. He describes how real world experiments have been designed to test Bell’s theorem, and how all tests to date have supported the predictions of quantum mechanics. He discusses the two major loopholes in experimental Bell tests, the locality and detection loopholes. (This book was written before the three loophole-free Bell experiments done in 2015. Perhaps he will add them to a future edition, since Gisin himself is a major contributor to the study of such loopholes.) He describes his 2008 experiment, which showed that any hidden superluminal communication between the two sides must be many times faster than the speed of light.

There are, of course, philosophical loopholes that are probably impossible to close, such as *superdeterminism*: the idea that all of Alice and Bob’s choices, as well as the seemingly random outcomes are determined from the beginning of the universe. Gisin briefly discusses a number of related topics, like the *Free Will Theorem* of Conway and Kochen, and outlines his more recent result (with collaborators Bancal et al.) that proves a remarkable extension of Bell’s theorem. Using 3- and 4-body correlations, they show that if correlations arise from influences propagating at any finite velocity, they must eventually either disagree with the predictions of quantum mechanics or allow superluminal communication (or both).

In addition to its central focus on Bell experiments and nonlocality, the book also discusses some applications of entanglement. There are two fairly brief chapters, one on random number generators and quantum cryptography and one on quantum teleportation, which hint at the large effort now being devoted to quantum-based technology.

The philosophical heart of the book, to which the author repeatedly returns, is this: if quantum mechanics violates Bell inequalities, then the randomness of quantum measurements is *not* due to ignorance, like the seeming randomness of a tossed coin or of thrown dice. Rather, it must be *true randomness*: new information that spontaneously appears out of nowhere. Gisin argues that because of its nonlocality, quantum mechanics is inconsistent with a deterministic, Newtonian world view. This argument–like all arguments in quantum foundations–has been disputed, but I have never seen it presented with such cogency as in this book.

While “Quantum Chance” does not assume knowledge of quantum mechanics, and derives all its arguments from first principles, it will not be an easy read for most laypeople. Several early chapters bristle with equations and tables, and the book draws on some math (like binary arithmetic and probability theory) that might be daunting to a mathematically unsophisticated reader. However, it is easily readable by technical readers who are not specialists in quantum theory. They will find it a concise and highly accessible introduction to Bell’s theorem, and to the ideas of entanglement and quantum nonlocality. And specialists will find it interesting as well, as clearly presenting the ideas of one of our deep thinkers about quantum theory.