Distribution of entanglement and correlations in all finite dimensions

Christopher Eltschka; Jens Siewert

doi:10.22331/q-2018-05-22-64

Distribution of entanglement and correlations in all finite dimensions

Christopher Eltschka¹ and Jens Siewert^2,3

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

Published:	2018-05-22, volume 2, page 64
Eprint:	arXiv:1708.09639v2
Scirate:	https://scirate.com/arxiv/1708.09639v2
Doi:	https://doi.org/10.22331/q-2018-05-22-64
Citation:	Quantum 2, 64 (2018).

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.

► BibTeX data

@article{Eltschka2018distributionof,
  doi = {10.22331/q-2018-05-22-64},
  url = {https://doi.org/10.22331/q-2018-05-22-64},
  title = {Distribution of entanglement and correlations in all finite dimensions},
  author = {Eltschka, Christopher and Siewert, Jens},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {64},
  month = may,
  year = {2018}
}

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[1] Waldemar Kłobus, Wiesław Laskowski, Tomasz Paterek, Marcin Wieśniak, and Harald Weinfurter, "Higher dimensional entanglement without correlations", The European Physical Journal D 73 2, 29 (2019).

[2] Christopher Eltschka, Felix Huber, Otfried Gühne, and Jens Siewert, "Exponentially many entanglement and correlation constraints for multipartite quantum states", Physical Review A 98 5, 052317 (2018).

[3] Sebastian Gartzke and Andreas Osterloh, "Generalized W state of four qubits with exclusively the three-tangle", arXiv:1712.08595, Physical Review A 98 5, 052307 (2018).

[4] Nikolai Wyderka, Felix Huber, and Otfried Gühne, "Constraints on correlations in multiqubit systems", Physical Review A 97 6, 060101 (2018).

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