A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios

• URL: http://arxiv.org/abs/2208.09236v2
• Date: Tue, 26 Nov 2024 02:02:03 GMT
• Title: A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
• Authors: Matty J. Hoban, Tom Drescher, Ana Belén Sainz,
• Abstract summary: Correlations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by textitassemblages of unnormalised quantum states, have recently caught the attention of the community. We introduce a hierarchy of tests where each level determines non-membership of the set of quantum assemblages or is inconclusive.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Correlations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by \textit{assemblages} of unnormalised quantum states, have recently caught the attention of the community, both from a foundational and an information-theoretic perspective. The set of quantum-realisable assemblages, or abbreviated to quantum assemblages, are those that arise from multiple parties performing local measurements on a shared quantum system. In general, deciding whether or not a given assemblage is a quantum assemblage, i.e. membership of the set of quantum assemblages, is a hard problem, and not always solvable. In this paper we introduce a hierarchy of tests where each level either determines non-membership of the set of quantum assemblages or is inconclusive. The higher the level of the hierarchy the better one can determine non-membership, and this hierarchy converges to a particular set of assemblages. Furthermore, this set to which it converges contains the quantum assemblages. Each test in the hierarchy is formulated as a semidefinite program. This hierarchy allows one to upper bound the quantum violation of a steering inequality and the quantum advantage provided by quantum EPR assemblages in a communication or information-processing task.

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