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International Journal of Quantum Information

Thermal quantum correlations in a two-qubit Heisenberg XYZ model with different magnetic fields

Zheng Hu, Yu‐Chen Wang, Xi-Wen Hou

Published Sep 1, 2015• 3 citations
Publisher

Abstract

Two kinds of thermal quantum correlations, measured respectively by quantum discord (QD) and the generalized negativity (GN), are studied for various magnetic fields, couplings, and temperatures in a two-qubit Heisenberg XYZ model. It is shown that QD and GN can exhibit a similar behavior in some regions of magnetic field, coupling, and temperature, while they behave in a contrary manner in other regions. For example, QD may increase with suitable magnetic fields, couplings, and temperature when GN decreases. QD is more robust against temperature than GN, and can reveal a kink at a suitable coupling at finite temperature while GN cannot. Moreover, a nearly unchanged QD or GN can be obtained in a large region of magnetic field, coupling, and temperature. These adjustable QD and GN via the varied magnetic field, coupling, and temperature may have significant applications in quantum information processing.

DOI
10.1142/s021974991550046x

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Two kinds of thermal quantum correlations, measured respectively by quantum discord (QD) and the generalized negativity (GN), are studied for various magnetic fields, couplings, and temperatures in a two-qubit Heisenberg XYZ model. It is shown that QD and GN can exhibit a similar behavior in some regions of magnetic field, coupling, and temperature, while they behave in a contrary manner in other regions. For example, QD may increase with suitable magnetic fields, couplings, and temperature when GN decreases. QD is more robust against temperature than GN, and can reveal a kink at a suitable coupling at finite temperature while GN cannot. Moreover, a nearly unchanged QD or GN can be obtained in a large region of magnetic field, coupling, and temperature. These adjustable QD and GN via the varied magnetic field, coupling, and temperature may have significant applications in quantum information processing.
The characterization of quantum discord (QD) has been well understood only for two-qubit states and is little known for mixed states beyond qubits. In this work, thermal quantum discord is studied for a qutrit system in different magnetic fields, where classical correlation and entanglement negativity are calculated for comparison. It is shown that the discord is more robust against temperature than the negativity. For a suitable region of magnetic field and its direction, the discord is non-zero while the negativity is zero. When the system is at a lower temperature, these three quantities, however, display a similar behavior for the varied field and direction, and their discontinuities come from crossovers between different ground states in the system. Moreover, the inequality between the quantum and classical correlations depends upon the system parameters as well as the temperature. In particular, both correlations are equal at a suitable field, direction, and temperature. Remarkably, such an equality remains for a strong field in the antiparallel direction, while both correlations in two-qubit systems are identical for any antiparallel field and temperature. These are useful for quantum information and understanding quantum correlations in qutrit mixed states.
We study the influences of the external magnetic field, temperature, and coupling parameter on the thermal quantum correlation in a two-qubit Heisenberg XY model, where the correlation is described in terms of two modified geometric discords and concurrence. It is shown that those three quantities behave similarly in the regions of lower temperature and weak magnetic field. However, the two geometric discords are more robust against temperature and magnetic field than the concurrence. Moreover, two geometric discords exhibit different behaviors under suitable conditions, that is, one discord increases as the magnetic field rises whereas the other discord decreases. In particular, the discord reveals the phenomenon of sudden change, while neither of other discord and concurrence displays such a phenomenon.
The investigation of quantum discord has mostly focused on two-qubit systems due to the complicated minimization involved in quantum discord for high-dimensional states. In this work, three geometric discords are studied for the thermal state in a two-qutrit system with various couplings, external magnetic fields, and temperatures as well, where the entanglement measured in terms of the generalized negativity is calculated for reference. It is shown that three geometric discords are more robust against temperature and magnetic field than the entanglement negativity. However, all four quantities exhibit a similar behavior at lower temperature and weak magnetic field. Remarkably, three geometric discords at finite temperature reveal the phenomenon of double sudden changes at different magnetic fields while the negativity does not. Moreover, the hierarchy among three discords is discussed. Those adjustable discords with the varied coupling, temperature, and magnetic field are useful for the understanding of quantum correlations in high-dimensional states and quantum information processing.
We investigate how quantum correlations [quantum discord (QD)] of a two-qubit one-dimensional XYZ\mathit{XYZ}XYZ Heisenberg chain in thermal equilibrium depend on the temperature TTT of the bath and also on an external magnetic field BBB. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with TTT when entanglement decreases, cases where QD increases with TTT even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite TTT. We also show that by properly tuning BBB or the interaction between the qubits we get nonzero QD for any TTT and we present an effect not seen for entanglement, the ``regrowth'' of thermal QD.
The thermal quantum discord (QD) is investigated in the two-qubit anisotropic Heisenberg XXZ model under an external non-uniform magnetic field along the Z-axis. We obtain the analytical expressions of the thermal QD and thermal entanglement measured by concurrence (C). It shows that for any temperature T, QD gradually decreases with the increase of non-uniform magnetic field |b|, in some regions where C increases while QD decreases. It is also found that thermal quantum discord does not vanish at finite temperatures, but concurrence vanishes completely at a critical temperature. It is shown that for a higher value of JZ, the system has a stronger QD. There is a critical magnetic field B c , which increases with the increasing b. QD decay monotonically (for B < B c ) when temperature T increases, or initially increases to some peaks and then decrease (for B > B c ).
We investigate how thermal quantum discord (QD) and classical correlations (CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on the temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behavior of QD differs in many unexpected ways from the thermal entanglement (EOF). For the nonuniform case ( B 1 = − B 2 ), we find that QD and CC are equal for all values of ( B 1 = − B 2 ) and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which QD and CC are equal. The specification of this class and the corresponding conditions are completely general and apply to any quantum system in a state in this class satisfying these conditions. We further find that the relative contributions of QD and CC can be controlled easily by changing the relative magnitudes of B 1 and B 2 . Finally, we connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environment.