The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.
Bibliographical noteFunding Information:
Engineering and Physical Sciences Research Council Royal Society Schweizerischer Nationalfonds zur F?rderung der Wissenschaftlichen Forschung National Centres of Competence in Research SwissMAP
We thank Marco Túlio Quintino for helpful discussions. B. D. M. J. acknowledges support from UK EPSRC (Grant No. EP/SO23607/1), P. S. from a Royal Society URF (UHQT), and I. S., R. U., and N. B. from the Swiss National Science Foundation (Project No. 2000021 192244/1 and NCCR SwissMap).
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