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arXiv:1204.2326

Effects of prepared states and Unruh temperature on Measurement-Induced-Nonlocality

Zehua Tian, Jiliang Jing

Published Apr 11, 2012• 0 citations
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Abstract

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 $\mathrm{A}$ and $\mathrm{I}$ decreases but the MIN between modes $\mathrm{A}$ and $\mathrm{II}$ increases. We prove that the parameters $c_i$ 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 $\mathrm{A}$ and $\mathrm{I}$, 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.

DOI
10.48550/arxiv.1204.2326

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Uniform acceleration induces a thermal response to the Minkowski vacuum and can thereby modify quantum correlations. For measurement-induced nonlocality (MIN), a form of nonclassical correlation distinct from entanglement, previous field-mode analyses of bosonic fields found that it decreases with increasing acceleration and vanishes in the infinite-acceleration limit. This raises the question of whether the disappearance of MIN is a generic consequence of the Unruh effect or depends on the physical description of the accelerated quantum system. To address this question, we study two uniformly accelerating Unruh-DeWitt detectors interacting with a massless scalar field. We find that the response of MIN to the Unruh temperature depends sensitively on the initial detector state: it can decrease monotonically, vanish at an intermediate temperature and subsequently recover, or increase monotonically. Moreover, for a broad class of initial states, MIN approaches a nonzero value in the high-temperature limit. These results show that the suppression of MIN under strong acceleration is not universal. Instead, Unruh-induced detector dynamics gives rise to a state-dependent response in which measurement-induced nonlocality can be suppressed, restored, or enhanced.
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.
We investigate the quantum correlation via measurement-induced-nonlocality (MIN) for Dirac particles in Garfinkle–Horowitz–Strominger (GHS) dilation space–time. It is shown that the physical accessible quantum correlation decreases as the dilation parameter increases monotonically. Unlike the case of scalar fields, the physical accessible correlation is not zero when the Hawking temperature is infinite owing to the Pauli exclusion principle and the differences between Fermi–Dirac and Bose–Einstein statistics. Meanwhile, the boundary of MIN related to Bell-violation is derived, which indicates that MIN is more general than quantum nonlocality captured by the violation of Bell-inequality. As a by-product, a tenable quantitative relation about MIN redistribution is obtained whatever the dilation parameter is. In addition, it is worth emphasizing that the underlying reason why the physical accessible correlation and mutual information decrease is that they are redistributed to the physical inaccessible regions.
We present a systematic and complementary study of quantum correlations near a black hole by considering measurement-induced nonlocality (MIN). The quantum measure of interest is discussed for the fermionic, bosonic and mixed fermion–boson modes on equal footing with respect to the Hawking radiation. The obtained results show that in the infinite Hawking temperature limit, the physically accessible correlations do not vanish only in the fermionic case. However, the higher frequency modes can sustain correlations for the finite Hawking temperature, with mixed systems being more sensitive towards the increase in the fermionic frequencies than the bosonic ones. Since the MIN for the latter modes quickly diminishes, the increased frequency may be a way to maintain nonlocal correlations for the scenarios at the finite Hawking temperature.