Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, ...
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Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and sufficient, and operational separability condition to determine whether an arbitrary quantum state is entangled or separable. In this paper, we show that whether a quantum state is entangled or not is determined by a threshold within the quantum state. We first introduce the concept of finer and optimal separable states based on the properties of separable states in the role of higher-level witnesses. Then we show that any bipartite quantum state can be decomposed into a convex mixture of its optimal entangled state and its optimal separable state. Furthermore, we show that whether an arbitrary quantum state is entangled or separable, as well as positive partial transposition (PPT) or not, is determined by the robustness of its optimal entangled state to its optimal separable state with reference to a crucial threshold. Moreover, for an arbitrary quantum state, we provide operational algorithms to obtain its optimal entangled state, its optimal separable state, its best separable approximation (BSA) decomposition, and its best PPT approximation decomposition. And the open question of how to calculate the BSA in high-dimension systems is partially done.
We present here results that strongly support the use of MERIS-based NIR-red algorithms as standard tools for estimating chlorophyll-a (chl-a) concentration in turbid productive waters. The study was carried out as on...
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We present here results that strongly support the use of MERIS-based NIR-red algorithms as standard tools for estimating chlorophyll-a (chl-a) concentration in turbid productive waters. The study was carried out as one of the steps in testing the potential of the universal applicability of previously developed NIR-red algorithms, which were earlier calibrated using a limited set of MERIS imagery and in situ data from the Azov Sea and the Taganrog Bay, Russia, and data that were synthetically generated using a radiative transfer model. We used an extensive set of MERIS imagery and in situ data collected over a period of three years in the Azov Sea and the Taganrog Bay for this validation task. We found that the two-band and three-band NIR-red algorithms gave consistently highly accurate estimates of chl-a concentration, with a mean absolute error of 4.32 mg m(-3) and 4.71 mg m(-3), respectively, and a root mean square error as low as 5.92 mg m(-3), for data with chl-a concentrations ranging from 1.09 mg m(-3) to 107.82 mg m(-3). This obviates the need for case-specific reparameterization of the algorithms, as long as the specific absorption coefficient of phytoplankton in the water does not change drastically, and presents a strong case for the use of NIR-red algorithms as standard algorithms that can be routinely applied for near-real-time quantitative monitoring of chl-a concentration in the Azov Sea and the Taganrog Bay, and potentially elsewhere, which will be a real boon to ecologists, natural resource managers and environmental decision-makers. (c) 2012 Elsevier Inc. All rights reserved.
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