Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins

TL;DR

This paper investigates how peripheral entanglement in a star network of spins grows logarithmically with size under noisy measurements, revealing effects of anisotropy and system limits.

Contribution

It demonstrates the conditions under which logarithmic growth of localizable bipartite entanglement occurs in a star network with noisy measurements, including anisotropy effects and different system limits.

Findings

Logarithmic growth of LBPE with periphery size in certain conditions.

Anisotropy suppresses LBPE growth, which can be mitigated by magnetic fields.

Growth persists across all noise levels in the large-periphery limit.

Abstract

In a star-network of qubits interacting via Heisenberg interaction of XYZ-type, we demonstrate a logarithmic growth of the localizable bipartite peripheral entanglement with increasing periphery-size and vanishing xy-anisotropy. This feature disappears when xy-anisotropy becomes non-zero, exhibiting an anisotropy effect, which can be negated by taking the system out of equilibrium by a qubit-local magnetic field. In the large-center and the competing-center limits of the model, the behaviour of LBPE is qualitatively different from that of the large-periphery limit. Also, the bipartite peripheral entanglement computed via a partial trace-based approach behaves qualitatively similarly to the LBPE in the large periphery limit, while in the other two limits, it behaves differently. We further consider the generalized description of localizable entanglement using unsharp measurements, and demonstrate that the logarithmic growth of LBPE is present for all noise strengths in the large-periphery limit, while in the competing-center limit, it does not.