Postquantum common-cause channels: the resource theory of local operations and shared entanglement

David Schmid1,2, Haoxing Du1, Maryam Mudassar1, Ghi Coulter-de Wit1, Denis Rosset1, and Matty J. Hoban3

1Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
2Institute for Quantum Computing and Dept. of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
3Department of Computing, Goldsmiths, University of London, New Cross, London SE14 6NW, United Kingdom

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Abstract

We define the type-independent resource theory of local operations and shared entanglement (LOSE). This allows us to formally quantify postquantumness in common-cause scenarios such as the Bell scenario. Any nonsignaling bipartite quantum channel which cannot be generated by LOSE operations requires a $\textit{postquantum common cause}$ to generate, and constitutes a valuable resource. Our framework allows LOSE operations that arbitrarily transform between different types of resources, which in turn allows us to undertake a systematic study of the different manifestations of postquantum common causes. Only three of these have been previously recognized, namely postquantum correlations, postquantum steering, and non-localizable channels, all of which are subsumed as special cases of resources in our framework. Finally, we prove several fundamental results regarding how the type of a resource determines what conversions into other resources are possible, and also places constraints on the resource's ability to provide an advantage in distributed tasks such as nonlocal games, semiquantum games, steering games, etc.

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[2] Denis Rosset, David Schmid, and Francesco Buscemi, "Type-Independent Characterization of Spacelike Separated Resources", Physical Review Letters 125 21, 210402 (2020).

[3] Martin Plávala, "General probabilistic theories: An introduction", arXiv:2103.07469.

[4] Paulo J. Cavalcanti, John H. Selby, Jamie Sikora, Thomas D. Galley, and Ana Belén Sainz, "Witworld: A generalised probabilistic theory featuring post-quantum steering", arXiv:2102.06581.

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