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Journal of Quantum Information Science

Measurement-Induced Nonlocality and Geometric Discord in the Spin-Boson Model

Guoyou Wang, Zi-Long Fan, Hao‐Sheng Zeng

Published Jan 1, 2013• 0 citations
Publisher

Abstract

Dynamics of measurement-induced-nonlocality (MIN) and geometric measure of discord (GD) in the spin-boson model is studied. Analytical results show that for two large classes of initial states, MINs are equal but GDs are different. At the end of evolution, MIN and GD initially stored in the spin system transfer completely to reservoirs. The quantum beats for MIN and GD are also found which are the results of quantum interference between two local non-Markovian dynamics via quantum correlation.

DOI
10.4236/jqis.2013.31008

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Dynamics of measurement-induced-nonlocality (MIN) and geometric measure of discord (GD) in the spin-boson model is studied. Analytical results show that for two large classes of initial states, MINs are equal but GDs are different. At the end of evolution, MIN and GD initially stored in the spin system transfer completely to reservoirs. The quantum beats for MIN and GD are also found which are the results of quantum interference between two local non-Markovian dynamics via quantum correlation.
We analyze the dynamics of geometric measure of discord (GMOD) and measurement-induced non-locality (MIN) in the presence of initial system—reservoir correlations without Born and Markov approximation. Although the initial system—environment states have the same reduced density matrices for both the system and environment, the effects of different initial system—environment correlations have been shown to fundamentally alter the time evolution of GMOD and MIN between two quantum systems in both Markovian and non-Markovian regimes. In general, both GMOD and MIN experience a sudden increase for initially quantum-correlated states, and a sudden decrease for classical-correlated states before they reach the same stationary values with initially factorized states.
How the prepared states and Unruh effect affect Measurement-Induced-Nonlocality (MIN) is studied. We show that, as the Unruh temperature increases, the MIN between modes A\mathrm{A}A and I\mathrm{I}I decreases but the MIN between modes A\mathrm{A}A and II\mathrm{II}II increases. We prove that the parameters cic_ici​ which decide initial prepared states affect not only the values of the MIN, but also the dynamical behavior of it. By comparing the MIN with the maximal expectation values of CHSH inequality and geometric discord between modes A\mathrm{A}A and I\mathrm{I}I, we also find that the MIN is more general than the quantum nonlocality related to violation of Bell's inequalities, and its values is always equal or bigger than that of the geometric discord.
We explore the dynamics of spin-boson model for the Ohmic bath by employing the master equation approach and obtain an explicit expression of reduced density matrix. We also calculate the geometric phases of the spin-boson model by making use of the analytical results and discuss how the dissipative bosonic environment affects geometric phases. Furthermore, we investigate the dynamics of quantum discord and entanglement of two qubits each locally interacting with its own independent bosonic environments. It is found that the decay properties of quantum discord and entanglement are sensitive to the choice of initial state's parameter and coupling strength between system and bath.
Recent studies show that two completely distinct fields as quantum information and string theory realization can be related and share some of the same properties. So, the knowledge on quantum information of some special quantum systems provides new insights on the sting theory. We analytically study geometric discord and measurement induced nonlocality for a Horodeckis' 33 bound entangled state to find quantum correlation. We find that there is a simultaneous sudden change point in the geometric discord and the measurement-induced nonlocality in the region of the bound entangled states, which is considerable. Moreover, we investigate the lower bound of geometric discord and the upper bound of measurement-induced nonlocality for this system. This study leads to some new and interesting novel results as well.
The dynamics of geometric discord (GD) and its transfer in a dissipative system consisting of two independent atom-cavity-reservoir subsystems under the strong coupling and the weak coupling regimes is studied. It is shown that the GD of the atoms and the cavities oscillatorily decays to zero while the reservoirs begin to present nonzero geometric quantum discord already immediately after t = 0 in the strong coupling regime. However, in the weak coupling regime, the GD between the atoms progressively decays becoming zero and the discord between the reservoirs arises from zero to a steady value, while the cavities remain almost uncorrelated during the evolution. We also show that the amount of GD contained in atoms and reservoirs depends on the purity p and it is proportional to p, the smaller the value of p the smaller the amount of GD. It is worth noting that, in both strong coupling and the weak coupling regimes, the results show that GD initially stored in the atoms will eventually be completely transferred to the reservoirs, independent of the parameters, but the transfer is mediated via the cavities in the strong coupling regime, while it is almost directly in the weak coupling regime.