Borromean states in discrete-time quantum walks

Marcin Markiewicz1, Marcin Karczewski1, and Pawel Kurzynski2

1International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-308 Gdansk, Poland
2Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University in Poznań, Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland

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In the right conditions, removing one particle from a multipartite bound state can make it fall apart. This feature, known as the "Borromean property", has been recently demonstrated experimentally in Efimov states. One could expect that such peculiar behavior should be linked with the presence of strong inter-particle correlations. However, any exploration of this connection is hindered by the complexity of the physical systems exhibiting the Borromean property. To overcome this problem, we introduce a simple dynamical toy model based on a discrete-time quantum walk of many interacting particles. We show that the particles described by it need to exhibit the Greenberger-Horne-Zeillinger (GHZ) entanglement to form Borromean bound states. As this type of entanglement is very prone to particle losses, our work demonstrates an intuitive link between correlations and Borromean properties of the system. Moreover, we discuss our findings in the context of the formation of composite particles.

Three Borromean rings are connected in a peculiar way. They are tightly bound together, but if one of them is cut and removed, the remaining two fall apart. This strange tripartite property gave rise to the concept of a Borromean state – a bound state of three quantum particles that falls apart if one particle is taken away. Such states can be observed in complex systems, whose analysis is not simple. To better understand their fundamental properties we propose a toy model, based on quantum walks, that allows us to observe formation of Borromean states between particles hopping in a one-dimensional discrete space-time. We find that in this case the Borromean property is intimately related to genuine multipartite entanglement.

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Cited by

[1] Adam S. Sajna and Paweł Kurzyński, "Collective dynamics of N -partite quantum systems: The role of entanglement, classical correlations, and interaction", Physical Review A 105 1, 012206 (2022).

[2] Xin Yan Fu, Zishi Jiang, and Sabyasachi Kar, "The <SUP>3</SUP>P<SUP>o</SUP> States of Exotic Molecular Ions with Exponential-Cosine-Screened Coulomb Potentials", Few-Body Systems 64 2, 15 (2023).

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