The resource theory of nonclassicality of channel assemblages

Beata Zjawin1, David Schmid1, Matty J. Hoban2,3, and Ana Belén Sainz1

1International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-309 Gdańsk, Poland
2Cambridge Quantum Computing Ltd
3Quantinuum LLC

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Abstract

When two parties, Alice and Bob, share correlated quantum systems and Alice performs local measurements, Alice's updated description of Bob's state can provide evidence of nonclassical correlations. This simple scenario, famously introduced by Einstein, Podolsky and Rosen (EPR), can be modified by allowing Bob to also have a classical or quantum system as an input. In this case, Alice updates her knowledge of the channel (rather than of a state) in Bob's lab. In this paper, we provide a unified framework for studying the nonclassicality of various such generalizations of the EPR scenario. We do so using a resource theory wherein the free operations are local operations and shared randomness (LOSR). We derive a semidefinite program for studying the pre-order of EPR resources and discover possible conversions between the latter. Moreover, we study conversions between post-quantum resources both analytically and numerically.

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Cited by

[1] David Schmid, Thomas C. Fraser, Ravi Kunjwal, Ana Belen Sainz, Elie Wolfe, and Robert W. Spekkens, "Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory", Quantum 7, 1194 (2023).

[2] Paulo J. Cavalcanti, John H. Selby, and Ana Belén Sainz, "Every nonsignaling channel is common-cause realizable", Physical Review A 109 4, 042211 (2024).

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