Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages

Beata Zjawin1, David Schmid1,2,3, Matty J. Hoban4,5, and Ana Belén Sainz1

1International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland
2Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
3Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
4Cambridge Quantum Computing Ltd, 9a Bridge Street, Cambridge, CB2 1UB, United Kingdom
5Department of Computing, Goldsmiths, University of London, New Cross, London SE14 6NW, United Kingdom

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Einstein-Podolsky-Rosen (EPR) steering is often (implicitly or explicitly) taken to be evidence for spooky action-at-a-distance. An alternative perspective on steering is that Alice has no causal influence on the physical state of Bob's system; rather, Alice merely updates her knowledge of the state of Bob's system by performing a measurement on a system correlated with his. In this work, we elaborate on this perspective (from which the very term 'steering' is seen to be inappropriate), and we are led to a resource-theoretic treatment of correlations in EPR scenarios. For both bipartite and multipartite scenarios, we develop the resulting resource theory, wherein the free operations are local operations and shared randomness (LOSR). We show that resource conversion under free operations in this paradigm can be evaluated with a single instance of a semidefinite program, making the problem numerically tractable. Moreover, we find that the structure of the pre-order of resources features interesting properties, such as infinite families of incomparable resources. In showing this, we derive new EPR resource monotones. We also discuss advantages of our approach over a pre-existing proposal for a resource theory of 'steering', and discuss how our approach sheds light on basic questions, such as which multipartite assemblages are classically explainable.

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Cited by

[1] Vinicius P. Rossi, Matty J. Hoban, and Ana Belén Sainz, "On characterising assemblages in Einstein-Podolsky-Rosen scenarios", Journal of Physics A Mathematical General 55 26, 264002 (2022).

[2] Beata Zjawin, David Schmid, Matty J. Hoban, and Ana Belén Sainz, "The resource theory of nonclassicality of channel assemblages", arXiv:2209.10177, (2022).

[3] Anna Jenčová, "Assemblages and steering in general probabilistic theories", Journal of Physics A Mathematical General 55 43, 434001 (2022).

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