6 research outputs found
Limits on correlations in networks for quantum and no-signaling resources
A quantum network consists of independent sources distributing entangled
states to distant nodes which can then perform entangled measurements, thus
establishing correlations across the entire network. But how strong can these
correlations be? Here we address this question, by deriving bounds on possible
quantum correlations in a given network. These bounds are nonlinear
inequalities that depend only on the topology of the network. We discuss in
detail the notably challenging case of the triangle network. Moreover, we
conjecture that our bounds hold in general no-signaling theories. In
particular, we prove that our inequalities for the triangle network hold when
the sources are arbitrary no-signaling boxes which can be wired together.
Finally, we discuss an application of our results for the device-independent
characterization of the topology of a quantum network.Comment: 15 pages, 6 figure
Towards a minimal example of quantum nonlocality without inputs
The network scenario offers interesting new perspectives on the phenomenon of
quantum nonlocality. Notably, when considering networks with independent
sources, it is possible to demonstrate quantum nonlocality without the need for
measurements inputs, i.e. with all parties performing a fixed quantum
measurement. Here we aim to find minimal examples of this effect. Focusing on
the minimal case of the triangle network, we present examples involving output
cardinalities of and . Finally, we discuss the prospects of
finding an example of quantum nonlocality in the triangle network with binary
outputs, and point out a connection to the Lovasz local lemma
Genuine quantum nonlocality in the triangle network
Quantum networks allow in principle for completely novel forms of quantum correlations. In particular, quantum nonlocality can be demonstrated here without the need of having various input settings, but only by considering the joint statistics of fixed local measurement outputs. However, previous examples of this intriguing phenomenon all appear to stem directly from the usual form of quantum nonlocality, namely via the violation of a standard Bell inequality. Here we present novel examples of 'quantum nonlocality without inputs', which we believe represent a new form of quantum nonlocality, genuine to networks. Our simplest examples, for the triangle network, involve both entangled states and joint entangled measurements. A generalization to any odd-cycle network is also presented. Finally, we conclude with some open questions