ABSTRACT We investigate the efficiency of quantum teleportation based on a pair of spin‐qubits from two infinite spin chains at temperature T, quantified by the maximum mean fidelity (MMF). For the XY model, we observe a non‐analytic behavior in the first‐order derivative of MMF near the Ising transition point as temperature approaches zero. We conduct a systematic analysis of the key ingredients governing the quantum criticality, including finite‐temperature scaling behavior and critical exponent. Regarding the anisotropy transition, we find that MMF exhibits phase‐dependent extremal behavior: it reaches a maximum in one phase and a minimum in the other. Furthermore, we demonstrate that MMF can also serve as a sensitive probe that accurately characterizes both the Ising transition and the anisotropy one under the long‐range teleportation protocol. For the extended Ising model, the first‐order derivative of MMF displays singular behavior at all critical points associated with topological quantum phase transition (TQPT) driven by different parameter. Through finite‐temperature scaling analysis, we verify the critical behavior and extract the corresponding critical exponent. The results not only confirm the occurrence of two‐type phase transitions simultaneously in a such system but also reveal that all these transitions belong to the Ising‐type transition.
Weiwen 维文 Cheng 程 (Fri,) studied this question.