A study on the relations between the topological parameter and entanglement

TL;DR

This paper explores how the topological parameter $d$ affects entanglement in quantum systems, revealing conditions for maximal entanglement, its behavior with varying $d$, and its impact on thermal entanglement and entanglement sudden death.

Contribution

It establishes the relationship between the topological parameter $d$ and entanglement measures, including maximal entanglement conditions and effects on thermal entanglement and ESD.

Findings

For $d=n$, all states are maximally entangled with $C=1$.

For $d eq n$, concurrence approaches zero as $d$ increases.

Parameter $d$ influences critical temperature and ESD behavior.

Abstract

In this paper, some relations between the topological parameter $d$ and concurrences of the projective entangled states have been presented. It is shown that for the case with $d=n$, all the projective entangled states of two $n$-dimensional quantum systems are the maximally entangled states (i.e. $C=1$). And for another case with $d\neq n$, $C$ both approach $0$ when $d\rightarrow +\infty$ for $n=2$ and $3$. Then we study the thermal entanglement and the entanglement sudden death (ESD) for a kind of Yang-Baxter Hamiltonian. It is found that the parameter $d$ not only influences the critical temperature $T_{c}$, but also can influence the maximum entanglement value at which the system can arrive at. And we also find that the parameter $d$ has a great influence on the ESD.