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arXiv:1712.01759 · International Journal of Quantum Information

Competition of direct and indirect sources of thermal entanglement in a spin-star network

Benedetto Militello, Anna Napoli

Published Jan 3, 2018• 2 citations
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Abstract

A spin-star system consisting of three peripheral two-state systems and a central one is considered, with the peripheral spins assumed to interact with each other, as well as with the central one. It is shown that such two couplings, each one being a thermal entanglement source, can significantly compete in the formation of quantum correlations in the thermal state to the point that they can destroy any thermal entanglement of the peripheral spins.

DOI
10.1142/s0219749918500077

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A spin-star system consisting of three peripheral two-state systems and a central one is considered, with the peripheral spins assumed to interact with each other, as well as with the central one. It is shown that such two couplings, each one being a thermal entanglement source, can significantly compete in the formation of quantum correlations in the thermal state to the point that they can destroy any thermal entanglement of the peripheral spins.
We investigate the quantum discord in the thermal states for a spin-star model consisting of three parties which include one central spin and the other two outer spins. Our results imply that the quantum correlation can be established between the two outer spins both of which interacting with the central spin independently. From the analysis, we find that the quantum discord and entanglement depends not only on the external magnetic field and the interaction strength but also on the anisotropy parameter and the temperature. Specially, the quantum discord is more robust than the quantum entanglement in the sense that the quantum discord lasts for higher temperatures than the entanglement does.
We exploit the tripartite negativity to study the thermal correlations in a tripartite system, that is, the three outer spins interacting with the central one in a spin–star system. We analyse the dependence of such correlations on the homogeneity of interactions, starting from the case where central–outer spin interactions are identical and then focusing on the case where the three coupling constants are different. We single out some important differences between the negativity and the concurrence.
We investigate analytically a star network of spins, in which all spins interact exclusively and continuously with a central spin through Heisenberg XXXXXX couplings of equal strength. We find that the central spin correlates and entangles the other spins at zero temperature to a degree that depends on the total number of spins. We find that the entanglement mediating capability of the central spin depends on the evenness or oddness of this number. In the limit of an infinite collection of spins, the difference between entanglement and correlations in terms of divisibility among multiple parties is clearly demonstrated. We also show that with a significant probability one can maximally entangle any two noncentral spins by measuring all the other spins (a process related to the recently introduced notion of localizable entanglement). This probability depends on the evenness and oddness of the total number of spins and remains substantial even for an infinite collection of spins. We show how symmetric multiparty states for optimal sharing and splitting of entanglement can be obtained as ground states of this system using a magnetic field. These states can then be mapped on to flying qubits for transmission to distant parties. We discuss a number of advantages of this mode of generation and distribution of entanglement over other standard methods.
Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.