Quantum marginal problem and incompatibility

Erkka Haapasalo; Tristan Kraft; Nikolai Miklin; Roope Uola

doi:10.22331/q-2021-06-15-476

Quantum marginal problem and incompatibility

Erkka Haapasalo^1,2, Tristan Kraft³, Nikolai Miklin⁴, and Roope Uola⁵

¹Centre for Quantum Technologies, National University of Singapore, Science Drive 2, Block S15-03-18, Singapore 117543
²Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
³Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
⁴Institute of Theoretical Physics and Astrophysics, National Quantum Information Center, Faculty of Mathematics, Physics and Informatics, University of Gdansk, 80-952 Gdańsk, Poland
⁵Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland

Published:	2021-06-15, volume 5, page 476
Eprint:	arXiv:1909.02941v3
Doi:	https://doi.org/10.22331/q-2021-06-15-476
Citation:	Quantum 5, 476 (2021).

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Abstract

One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even higher order dynamics. In this manuscript, we show that two seemingly different aspects of quantum incompatibility: the quantum marginal problem of states and the incompatibility on the level of quantum channels are in many-to-one correspondence. Importantly, as incompatibility of measurements is a special case of the latter, it also forms an instance of the quantum marginal problem. The generality of the connection is harnessed by solving the marginal problem for Gaussian and Bell diagonal states, as well as for pure states under depolarizing noise. Furthermore, we derive entropic criteria for channel compatibility, and develop a converging hierarchy of semi-definite programs for quantifying the strength of quantum memories.

► BibTeX data

@article{Haapasalo2021quantummarginal,
  doi = {10.22331/q-2021-06-15-476},
  url = {https://doi.org/10.22331/q-2021-06-15-476},
  title = {Quantum marginal problem and incompatibility},
  author = {Haapasalo, Erkka and Kraft, Tristan and Miklin, Nikolai and Uola, Roope},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {476},
  month = jun,
  year = {2021}
}

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