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
Doi:	https://doi.org/10.22331/q-2018-05-22-64
Citation:	Quantum 2, 64 (2018).

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Abstract

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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Cited by

[1] Christopher Eltschka and Jens Siewert, "Joint Schmidt-type decomposition for two bipartite pure quantum states", Physical Review A 101 2, 022302 (2020).

[2] 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).

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

[4] Christopher Eltschka and Jens Siewert, "MaximumN-body correlations do not in general imply genuine multipartite entanglement", Quantum 4, 229 (2020).

[5] Satoya Imai, Nikolai Wyderka, Andreas Ketterer, and Otfried Gühne, "Bound Entanglement from Randomized Measurements", Physical Review Letters 126 15, 150501 (2021).

[6] Pengwei Zhi and Yi Hu, "Demonstrate Absolutely Maximally Entangled of Four- and Eight-qubit States Inexistence via Simple Constraint Condition", International Journal of Theoretical Physics 60 9, 3488 (2021).

[7] Yu Guo, Lizhong Huang, and Yang Zhang, "Monogamy of quantum discord", Quantum Science and Technology 6 4, 045028 (2021).

[8] Paul Appel, Marcus Huber, and Claude Klöckl, "Monogamy of correlations and entropy inequalities in the Bloch picture", arXiv:1710.02473, Journal of Physics Communications 4 2, 025009 (2020).

[9] Christopher Eltschka, Marcus Huber, Simon Morelli, and Jens Siewert, "The shape of higher-dimensional state space: Bloch-ball analog for a qutrit", Quantum 5, 485 (2021).

[10] Jie Zhu, Meng-Jun Hu, Yue Dai, Yan-Kui Bai, S. Camalet, Chengjie Zhang, Chuan-Feng Li, Guang-Can Guo, and Yong-Sheng Zhang, "Realization of the tradeoff between internal and external entanglement", Physical Review Research 2 4, 043068 (2020).

[11] Felix Huber, "Positive maps and trace polynomials from the symmetric group", Journal of Mathematical Physics 62 2, 022203 (2021).

[12] 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).

[13] N Wyderka and O Gühne, "Characterizing quantum states via sector lengths", Journal of Physics A: Mathematical and Theoretical 53 34, 345302 (2020).

[14] 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).

[15] Yu Guo and Lin Zhang, "Multipartite entanglement measure and complete monogamy relation", Physical Review A 101 3, 032301 (2020).

[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).

The above citations are from Crossref's cited-by service (last updated successfully 2021-10-20 06:08:57) and SAO/NASA ADS (last updated successfully 2021-10-20 06:08:58). The list may be incomplete as not all publishers provide suitable and complete citation data.

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