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arXiv:2304.02448 · Physical Review A

Detecting quantum critical points at finite temperature via quantum teleportation

G A P Ribeiro, Gustavo Rigolin

Published May 25, 2023• 9 citations
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Abstract

We show that the quantum teleportation protocol is a powerful tool to study quantum phase transitions at finite temperatures. We consider a pair of spins from an infinite spin-1/2 chain ($XXZ$ model) in equilibrium with a reservoir at temperature $T$ as the resource used by Alice and Bob to implement the teleportation protocol. We show that the efficiency of this pair of spins to teleport a qubit is drastically affected after we cross a quantum critical point (QCP), even for high values of $T$. Also, we show that the present tool is as sharp as quantum discord (QD) to spotlight a QCP, where QD is the best finite $T$ QCP detector known to date. Contrary to QD, however, we show that the present tool is easier to compute theoretically and has a direct experimental and operational meaning.

DOI
10.1103/physreva.107.052420

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We show that the quantum teleportation protocol is a powerful tool to study quantum phase transitions at finite temperatures. We consider a pair of spins from an infinite spin-1/2 chain (XXZXXZXXZ model) in equilibrium with a reservoir at temperature TTT as the resource used by Alice and Bob to implement the teleportation protocol. We show that the efficiency of this pair of spins to teleport a qubit is drastically affected after we cross a quantum critical point (QCP), even for high values of TTT. Also, we show that the present tool is as sharp as quantum discord (QD) to spotlight a QCP, where QD is the best finite TTT QCP detector known to date. Contrary to QD, however, we show that the present tool is easier to compute theoretically and has a direct experimental and operational meaning.
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 comparatively study three of the most useful quantum information tools to detect quantum critical points (QCPs) when only finite temperature data are available. We investigate quantitatively how the quantum discord, the quantum-teleportation-based QCP detectors, and the quantum coherence spectrum pinpoint the QCPs of several spin-1/21/21/2 chains. We work in the thermodynamic limit (infinite number of spins) and with the spin chains in equilibrium with a thermal reservoir at temperature TTT. The models here studied are the XXZ model with and without an external longitudinal magnetic field, the Ising transverse model, and the XY model subjected to an external transverse magnetic field.
We show for the models here investigated that the teleportation-based quantum critical point (QCP) detectors can properly estimate the locations of the QCPs when we are not even close to the thermodynamic limit (infinite spin chains) and when we only have access to finite temperature data. Specifically, by working with spin chains with about ten qubits and in equilibrium with a thermal reservoir at temperature T, we show that it is possible to locate with an error of only a few percents the correct spots of the QCPs for almost all the models studied here. The spin chains we investigate are given by the XXZ model with or without an external longitudinal magnetic field as well as the XX model, the XY model and the Ising model, all of them subjected to an external transverse magnetic field.
We compute the quantum correlation [quantum discord (QD)] and the entanglement (EOF) between nearest-neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EOF and other thermodynamic quantities, spotlight the critical points associated with quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.
We extend the program initiated by T. Werlang et al. [Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ\mathit{XXZ}XXZ model, the XY\mathit{XY}XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest neighbors and also study the behavior of entanglement and quantum discord for second nearest neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite TTT, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.
We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions (QPT) that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a QPT.