Agreement and disagreement in a non-classical world.

The Agreement Theorem Aumann (1976 Ann. Stat. 4, 1236-1239. (doi:10.1214/aos/1176343654)) states that if two Bayesian agents start with a common prior, then they cannot have common knowledge that they hold different posterior probabilities of some underlying event of interest. In short, the two agents cannot 'agree to disagree'. This result applies in the classical domain where classical probability theory applies. But in non-classical domains, such as the quantum world, classical probability theory does not apply. Inspired principally by their use in quantum mechanics, we employ signed probabilities to investigate the epistemics of the non-classical world. We find that here, too, it cannot be common knowledge that two agents assign different probabilities to an event of interest. However, in a non-classical domain, unlike the classical case, it can be common certainty that two agents assign different probabilities to an event of interest. Finally, in a non-classical domain, it cannot be common certainty that two agents assign different probabilities, if communication of their common certainty is possible-even if communication does not take place. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

Asymptotic Survival of Genuine Multipartite Entanglement in Noisy Quantum Networks Depends on the Topology.

The study of entanglement in multipartite quantum states plays a major role in quantum information theory and genuine multipartite entanglement signals one of its strongest forms for applications. However, its characterization for general (mixed) states is a highly nontrivial problem. We introduce a particularly simple subclass of multipartite states, which we term pair-entangled network (PEN) states, as those that can be created by distributing exclusively bipartite entanglement in a connected network. We show that genuine multipartite entanglement in a PEN state depends on both the level of noise and the network topology and, in sharp contrast to the case of pure states, it is not guaranteed by the mere distribution of mixed bipartite entangled states. Our main result is a markedly drastic feature of this phenomenon: the amount of connectivity in the network determines whether genuine multipartite entanglement is robust to noise for any system size or whether it is completely washed out under the slightest form of noise for a sufficiently large number of parties. This latter case implies fundamental limitations for the application of certain networks in realistic scenarios, where the presence of some form of noise is unavoidable. To illustrate the applicability of PEN states to study the complex phenomenology behind multipartite entanglement, we also use them to prove superactivation of genuine multipartite nonlocality for any number of parties.

Genuine Multipartite Nonlocality Is Intrinsic to Quantum Networks.

Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite entangled states are genuine multipartite nonlocal in the sense that measurements can be found on finitely many copies of any genuine multipartite entangled state to yield a genuine multipartite nonlocal behavior. Our results pave the way toward feasible manners of generating genuine multipartite nonlocality using any connected network.

Resource Theory of Entanglement with a Unique Multipartite Maximally Entangled State.

Entanglement theory is formulated as a quantum resource theory in which the free operations are local operations and classical communication (LOCC). This defines a partial order among bipartite pure states that makes it possible to identify a maximally entangled state, which turns out to be the most relevant state in applications. However, the situation changes drastically in the multipartite regime. Not only do there exist inequivalent forms of entanglement forbidding the existence of a unique maximally entangled state, but recent results have shown that LOCC induces a trivial ordering: almost all pure entangled multipartite states are incomparable (i.e., LOCC transformations among them are almost never possible). In order to cope with this problem we consider alternative resource theories in which we relax the class of LOCC to operations that do not create entanglement. We consider two possible theories depending on whether resources correspond to multipartite entangled or genuinely multipartite entangled (GME) states and we show that they are both nontrivial: no inequivalent forms of entanglement exist in them and they induce a meaningful partial order (i.e., every pure state is transformable to more weakly entangled pure states). Moreover, we prove that the resource theory of GME that we formulate here has a unique maximally entangled state, the generalized GHZ state, which can be transformed to any other state by the allowed free operations.

Observers of quantum systems cannot agree to disagree.

Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the postquantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann's seminal Agreement Theorem states that two observers (of classical systems) cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for observers of quantum systems, while we construct examples of (postquantum) no-signaling boxes where observers can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.