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

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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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[16] Xinwei Zha, Irfan Ahmed, Da Zhang, and Yanpeng Zhang, "Generalized monogamy linear entropy relations for multi-qubit pure states", Laser Physics 30 3, 035201 (2020).

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