Quantum cryptography exploits principles of quantum physics for the secure processing of
information. A prominent example is secure communication, ie, the task of transmitting …

This article surveys quantum computational complexity, with a focus on three fundamental
notions: polynomial-time quantum computations, the efficient verification of quantum proofs …

This largely self-contained book on the theory of quantum information focuses on precise
mathematical formulations and proofs of fundamental facts that form the foundation of the …

We show that quantum theory allows for transformations of black boxes that cannot be
realized by inserting the input black boxes within a circuit in a predefined causal order. The …

Causal modelling provides a powerful set of tools for identifying causal structure from
observed correlations. It is well known that such techniques fail for quantum systems, unless …

A thorough exposition of quantum computing and the underlying concepts of quantum
physics, with explanations of the relevant mathematics and numerous examples. The …

Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions
of different states. However, it has recently been appreciated that quantum mechanics also …

There has been recent promising experimental and theoretical evidence that quantum
computational tools might enhance the precision and efficiency of physical experiments …

Our common understanding of the physical world deeply relies on the notion that events are
ordered with respect to some time parameter, with past events serving as causes for future …

Shannon's theory of information was built on the assumption that the information carriers
were classical systems. Its quantum counterpart, quantum Shannon theory, explores the …