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Everett's relative-state construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett's one in the Schrödinger picture, makes manifest the locality of Everettian multiplicity, its inherently approximative nature and its origin in certain kinds of entanglement and locally inaccessible information. (By Everettian , we are referring not only to Everett's own work, but also to versions of quantum theory that elaborate and refine his. The notion of relative states first appeared in Everett (Everett 1973 In The many worlds interpretation of quantum mechanics (eds BS DeWitt, N Graham)). We are proposing a formalism for relative states that is more detailed and more illuminating than Everett's.) Our construction also allows us to give a more precise definition of an Everett ‘universe’, under which it is fully quantum, not quasi-classical, and we compare the Everettian decomposition of a quantum state with the foliation of a space–time.

Claims that the standard procedure for testing scientific theories is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing. Refuting those claims by correcting those misconceptions leads to an improved theory of scientific methodology (based on Popper׳s) and testing, which allows various simplifications, notably the elimination of everything probabilistic from the methodology (‘Bayesian’ credences) and from fundamental physics (stochastic processes).

Two of us (Marletto and Vedral 2017 Phys. Rev. Lett. 119 240402) recently showed how the quantum character of a physical system, in particular the gravitational field, can in principle be witnessed without directly measuring observables of that system, solely by its ability to mediate entanglement between two other systems. Here we propose a variant of that scheme, where the entanglement is again generated via gravitational interaction, but now between two particles both at sharp locations (very close to each other) but each in a superposition of two different masses. We discuss an in principle example using two hypothetical massive, neutral, weakly-interacting particles generated in a superposition of different masses. The key property of such particles would be that, like neutrinos, they are affected only by weak nuclear interactions and gravity.

The idea of a "doppelganger" (a "double" of a person) is a frequent theme of science fiction.

The structure of the multiverse is determined by information flow., 21 pages, 3 illustrations

We propose a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible—i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).

All information in quantum systems is, notwithstanding Bell's theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through 'classical' (i.e. decoherent) information channels., Comment: PostScript version now available: http://www.qubit.org/people/patrickh/Papers/InformationFlow.ps

In a previous paper, Hayden and I ( Deutsch & Hayden 2000 Proc. R. Soc. Lond. A 456 , 1759–1774. ( doi:10.1098/rspa.2000.0585 )) proved, using the Heisenberg picture, that quantum physics satisfies Einstein's criterion of locality. Wallace and Timpson ( Wallace & Timpson 2007 Found. Phys. 37 , 951–955. ( doi:10.1007/s10701-007-9135-7 )) have argued that certain transformations of the Heisenberg-picture description of a quantum system must be regarded as leaving invariant the factual situation being described, and that taking this into account reveals that Einstein's criterion is violated after all. Here, I vindicate the proof and explain some misconceptions that have led to this and other criticisms of it.

The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory.

Douglas Hofstadter's writing talent makes his love of paradox contagious. Reading I Am a Strange Loop inclines one to see whimsical connections, language games and self-reference everywhere. Part of Hofstadter invades one's brain and starts thinking there in its own right – a phenomenon that is itself a theme of the book. Hofstadter, therefore, is in effect co-writing this review, inclining it towards paradox. Which may be why my method of urging you to read the book will itself be paradoxical: I shall summarize why I find it ultimately unconvincing.

Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an `entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and single-qubit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted message., Comment: 13 pages, Latex including 2 postcript files included using psfig macros

Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting non--classical properties. We describe a simple quantum logic gate, the quantum controlled--NOT, and analyse some of its applications. We discuss two possible physical realisations of the gate; one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole--dipole interaction., 5 pages, RevTeX, two figures in a uuencoded, compressed file

Information is physical and any processing of information is always performed by physical means – an innocent-sounding statement, but its consequences are anything but trivial. In the last few years there has been an explosion of theoretical and experimental innovations which, their discoverers claim, are creating a fundamental new discipline: a distinctively quantum theory of information.

What are the three best popular-science books? My three favourites are Longitude by Dava Sobel, The Labyrinth of Time: Introducing the Universe by Michael Lockwood and The Neptune File: Planet Detectives and the Discovery of Worlds Unseen by Tom Standage.

There is a spectre haunting this book – the spectre of John Horgan, the journalist whose successful book The End of Science tweaked the collective nose of the scientific community when it was published in 1996. Horgan claimed that everything of fundamental importance that can be known to science is already known, or soon will be. He is nowhere mentioned in What Remains to be Discovered (except on the back cover, as rather ambiguous reviewer), yet I would be surprised if John Maddox did not intend to write this book as an antidote to Horgan.

Wheeler's idea that physical “laws” would not appear in a truly fundamental description of nature is critically examined.

It is shown that the laws of physics impose no fundamental bound on the rate at which information can be processed. Recent claims that quantum effects impose such bounds are discussed and shown to be erroneous.

The object of this Letter is to show that except in the case of canonically conjugate observables, the generalized Heisenberg inequality does not properly express the quantum uncertainty principle. It is, in general, too weak. An inequality is obtained which does express the principle.