We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment. In addition, concepts that are distinct in the conventional formalism become unified: Channels, sets of states, and positive operator valued measures are all seen to be instances of conditional states; the action of a channel on a state, ensemble averaging, the Born rule, the composition of channels, and nonselective state-update rules are all seen to be instances of belief propagation. Using a quantum generalization of Bayes' theorem and the associated notion of Bayesian conditioning, we also show that the remote steering of quantum states can be described within our formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences. Finally, we show that previous arguments for interpreting the projection postulate as a quantum generalization of Bayesian conditioning are based on a misleading analogy and that it is best understood as a combination of belief propagation (corresponding to the nonselective state-update map) and conditioning on the measurement outcome.

T owards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality) in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey-Barrett-Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey-Barrett-Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge); Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey-Barrett-Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey-Barrett-Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey-Barrett-Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67-155.This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY-3.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Quanta |