Abstract
In this paper, we study a system with two interacting qubits described by the Heisenberg model with dissipative terms, and analyze decay dynamics and the steady-state of geometric quantum discords. Our results indicate that we can ignore the interaction force in the z-direction and adjust the parameters to change the loss of quantum correlation with time when the initial state satisfies some conditions. Moreover, we show that after a long enough period of time, unlike other parameters, the energy and the intensity of the non-uniform magnetic field do not affect the steady-state.
Highlights
In this paper, we study a system with two interacting qubits described by the Heisenberg model with dissipative terms, and analyze decay dynamics and the steady-state of geometric quantum discords
After quantum discord was firstly proposed by Ollivier and Zurek[2] and by Henderson and Vedral[12] respectively, a series of discord-like quantum correlations were proposed which exhibit different properties when characterizing the dynamics of the same quantum system and have become important resources in quantum theory
As one of discord-like quantum correlations, the geometric quantum discord, which will be used in this paper, has been widely concerned because it is easier to calculate and useful
Summary
Discussing the non-classicality of a composite system, which we collectively refer to as quantum correlation, is important to find a way to measure its deviation from the classical system. The following four geometric quantum discords are basic and important examples[5, 15, 16]: Hilbert–Schmidt distance discord. Hilbert–Schmidt distance discord is one of the metrics proposed to substitute quantum discord and is widely used because of its easy calculation. For the case of a two-level two-qubit, the density matrix ρ has the following form. In18, it gives the analytical solution of the two-qubit It does not have the problem about the Hilbert–Schmidt distance discord above: DHe(ρAB ⊗ ρC ) = DHs(ρAB)Tr. According to[19], it avoids the problem about the Hilbert–Schmidt distance discord above. The closed formulae for Bures distance discords of 2-qubit Bell diagonal state are given in[19, 20]
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