Entanglement dynamics between Ising spins and a central ancilla

We investigate competing entanglement dynamics in an Ising spin chain coupled to an external central ancilla qudit. In studying the real-time behavior following a quench from an unentangled spin-ancilla state, we find that the ancilla entanglement entropy S-vN;A tracks the dynamical phase transition in the underlying spin system. In this composite setting, purely spin-spin entanglement metrics such as mutual information and quantum Fisher information (QFI) decay as the ancilla entanglement entropy grows. We define multipartite entanglement loss (MEL) as the difference between collective magnetic fluctuations and QFI, which is zero in the pure spin chain limit. MEL directly quantifies the ancilla's effect on the development of spin-spin entanglement. One of our central results is that we find M-el (t) proportional to e(SvN;A(t)). Our results provide a platform for exploring composite system entanglement dynamics and suggest that MEL serves as a quantitative estimate of information entropy shared between collective spins and the ancilla qudit. Our results present a framework that connects physical spin fluctuations, QFI, and bipartite entanglement entropy between collective quantum systems.

Automated summary

This study investigates competing entanglement dynamics between a one-dimensional Ising spin chain and an external ancilla qudit system. The results show that the entanglement entropy of the ancilla can track the dynamical phase transition in the underlying spin system. It is found that purely spin-spin entanglement metrics decay as the entanglement entropy of the ancilla increases. The study also introduces the concept of multipartite entanglement loss (MEL), which quantifies the effect of the ancilla on the development of spin-spin entanglement.