Measurement-induced phase transition arises from the competition between a deterministic quantum evolution and a repeated measurement process. We explore the measurement-induced phase transition through the Quantum Fisher Information in two different metrological scenarios. We demonstrate through the scaling behavior of the quantum Fisher information the transition of the multi-partite entanglement across the phases. In analogy with standard quantum phase transition, we reveal signature of a measurement-induced phase transition in the non-analytic behaviour of the quantum Fisher information as the measurement strength approaches the critical value. Our results offer novel insights into the features of a quantum systems undergoing measurement-induced phase transition and indicate potential avenues for further exploration in the field of quantum physics.
The ground state of interacting spin chains in external magnetic fields can undergo a quantum phase transition (QPT) characterized by dramatic changes at a critical value of the magnetic field. In this paper, we use Bell-type inequalities to study the multipartite correlations (including multipartite entanglement and multipartite nonlocality in an
n-spin subsystem) in the QPT of an infinite
XY chain. An efficient numerical optimization procedure is proposed to figure out the violation measure
Mn of the inequalities. For $n\ensuremath{\le}7$, the magnetic-field ($\ensuremath{\lambda}$) dependence of
Mn is studied. We find the derivative of
Mn is divergent exactly at the QPT point ${\ensuremath{\lambda}}_{c}=1$ for any
n. In addition, with the increase of
n,
Mn converges quickly for $\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$ and converges very slowly for $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}$, which can be regarded as another signal for the QPT. Furthermore, in the vicinity of ${\ensuremath{\lambda}}_{c}$, high-order Bell-type inequalities will be violated as long as
n is large enough. This indicates that high-level multipartite correlation will be present when the system is in the vicinity of the QPT point. Nevertheless, genuine
n-partite entanglement or genuine
n-partite nonlocality is not observed in the QPT.
We find non-localities, violation of local realism, in the many-body ground states of spin-1 XXZ chain with on-site anisotropy. In order to identify the non-localities in higher spin systems, we exploit the generalized version of multipartite Bell-type inequalities which characterize symmetric entangled states under the most general settings via combination of high-order correlations. For a given set of unbiased measurements, we obtain a sharp violation of the multipartite Bell-type inequality at the vicinity of the quantum criticality, a type of the first-order, in the regime of large exchanges and strong on-site anisotropies. It signifies that impossibility of local realistic picture is manifested when a system is subjected to quantum phase transition between weekly entangled states via GHZ-like state. Our results provide the first extendible picture on the relationship between the impossibility of local realistic model and many-body quantum phases in higher-spin system as the observable identifies measurable quantities to detect the non-locality on a particular many-body quantum state.