Distribution of entanglement and correlations in all finite dimensions

Christopher Eltschka1 and Jens Siewert2,3

1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
2Departamento de Química Física, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
3IKERBASQUE Basque Foundation for Science, E-48013 Bilbao, Spain

The physics of a many-particle system is determined by the correlations in its quantum state. Therefore, analyzing these correlations is the foremost task of many-body physics. Any 'a priori' constraint for the properties of the global vs. the local states-the so-called marginals-would help in order to narrow down the wealth of possible solutions for a given many-body problem, however, little is known about such constraints. We derive an equality for correlation-related quantities of any multipartite quantum system composed of finite-dimensional local parties. This relation defines a necessary condition for the compatibility of the marginal properties with those of the joint state. While the equality holds both for pure and mixed states, the pure-state version containing only entanglement measures represents a fully general monogamy relation for entanglement. These findings have interesting implications in terms of conservation laws for correlations, and also with respect to topology.

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► Cited by (beta)

[1] Christopher Eltschka, Felix Huber, Otfried Gühne, Jens Siewert, "Exponentially many entanglement and correlation constraints for multipartite quantum states", Physical Review A 98, 052317 (2018).

[2] Sebastian Gartzke, Andreas Osterloh, "Generalized W state of four qubits with exclusively the three-tangle", Physical Review A 98, 052307 (2018).

[3] Nikolai Wyderka, Felix Huber, Otfried Gühne, "Constraints on correlations in multiqubit systems", Physical Review A 97, 060101 (2018).

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