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Annalen der Physik

Detecting Conventional and Topological Phase Transitions via Quantum Teleportation

Weiwen 维文 Cheng 程

Published May 1, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1002/andp.70220

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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.
We explore quantum speed limit time τQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that τQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field λ or the anisotropy γ of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of τQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the three-site interaction α or its anisotropy δ. Additionally, we also investigate τQSL for arbitrary time-evolution state in the whole dynamics process and find that τQSL exhibits a behavior of oscillation at non-critical points. However, τQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points.
We study the relationship between the quantum Fisher information (QFI) of spin pairs and the topological quantum phase transitions (TQPTs) of the extended XY model driven by the anisotropies of the nearest-neighbor and the next-nearest-neighbor spins, the transverse magnetic field, and the three-spin interaction. We find that the first derivative of QFI can correctly characterize the TQPTs at absolute zero temperature. Meanwhile, the impacts of the thermal fluctuations and the site distance of spin pairs on the critical behaviors of the QFI are studied. It is found that the first derivative of QFI for the nearest neighbor or the long-distance spin pairs can only correctly characterize the critical points of the TQPTs at sufficiently low temperature. Remarkably, when the anisotropy of the nearest-neighbor and the next-nearest-neighbor spins are the driven parameters and the site distance R=5R=5R=5, the QFI itself can characterize the TQPTs at absolute zero temperature.
In previous work [Phys. Rev. A 107, 052420 (2023)] we showed that the quantum teleportation protocol can be used to detect quantum critical points (QCPs) associated with a couple of different classes of quantum phase transitions, even when the system is away from the absolute zero temperature (T=0T=0T=0). Here, working in the thermodynamic limit (infinite chains), we extend the previous analysis for several other spin-12\frac{1}{2}21​ models. We investigate the usefulness of the quantum teleportation protocol to detect the QCPs of those models when the temperature is either zero or greater than zero. The spin chains we investigate here are described by the XXZXXZXXZ model, the XYXYXY model, and the Ising model, all of them subjected to an external magnetic field. Specifically, we use a pair of nearest-neighbor qubits from an infinite spin chain at thermal equilibrium with a reservoir at temperature TTT as the resource to execute the quantum teleportation protocol. We show that the ability of this pair of qubits to faithfully teleport an external qubit from the chain is dramatically affected as we cross the QCPs related to the aforementioned models. The results here presented together with the ones of aforementioned work suggest that the quantum teleportation protocol is a robust and quite universal tool to detect QCPs even when the system of interest is far from the absolute zero temperature.
We use two-site quantum nonlocality to identify the topological quantum phase transitions (TQPTs) of the extended Ising model driven by varying system parameters. We investigate how the system parameters, including the anisotropies of the nearest-neighbor and the next-nearest-neighbor spin pairs, the transverse magnetic field, and the three-spin interaction, affect the quantum nonlocality. We show that the nonlocality cannot mark any TQPTs while its first derivative can perfectly characterize the TQPTs. By making the influences of the thermal fluctuations and the site distance of spin pairs on the critical behavior of the TQPTs analysis, we show that the sufficiently low temperature has a slight impact on the features of nonlocality and its first derivative while the site distance of spin pairs can significantly alter the properties of nonlocality and its first derivative. We further present the energy spectra and the trajectories of the winding vectors of the model to demonstrate that the quantum nonlocality can be employed to successfully signalize the TQPTs.
ABSTRACT The ground‐state phase transition for the spin‐1/2 Heisenberg chain with ‐direction dimerized anisotropy is investigated by exploiting the infinite time‐evolving block decimation algorithm. Phase boundaries are identified by examining the von Neumann entropy, entanglement spectrum, and several of fidelity indicators. The phase diagram features the existence of a tri‐critical point, which signifies the complete convergence of the transition boundaries separating the Odd‐Haldane, Even‐Haldane, and Néel phases. Specifically, the high‐precision fit of the Tomonaga–Luttinger liquid parameter provides evidence for a Tomonaga–Luttinger liquid phase line which splits the Odd‐Haldane and Even‐Haldane phases. Along this critical line, it is found that the critical exponent exhibits a variation with the bond dimerization strength, which is according to a power‐law scaling. This provides a crucial theoretical framework for analyzing critical behaviors associated with topological phase transitions in quantum many‐body systems. From the odd and even string order parameters and the non‐local Néel order parameter, the Haldane phases and the Néel phase are characterized. Furthermore, the central charge and critical exponent are identified by performing a scaling analysis of finite correlation length and order parameters, indicating that the phase transition between the Haldane phases and Néel phase belongs to the classical Ising universality class, as well as a Gaussian phase transition between two types of Haldane phases.
A useful approach to characterize and identify quantum phase transitions lies in the concept of multipartite entanglement. In this paper, we consider well-known measures of multipartite (global) entanglement, i.e., average linear entropy of one-qubit and two-qubit reduced density matrices, in order to study topological quantum phase transition (TQPT) in the Kitaev Toric code Hamiltonian with a nonlinear perturbation. We provide an exact mapping from aforementioned measures in the above model to internal energy and energy-energy correlations in the classical Ising model. Accordingly, we find that the global entanglement shows a continuous and sharp transition from a maximum value in the topological phase to zero in the magnetized phase in a sense that its first-order derivative diverges at the transition point. In this regard, we conclude that not only can the global entanglement serve as a reasonable tool to probe quantum criticality at TQPTs, but it also can reveal the highly entangled nature of topological phases. Furthermore, we also introduce a conditional version of global entanglement which becomes maximum at the critical point. Therefore, regarding a general expectation that multipartite entanglement reaches maximum value at the critical point of quantum many-body systems, our result proposes that the conditional global entanglement can be a good measure of multipartite entanglement in TQPTs.