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The last two decades have witnessed significant progress on the understanding the quantum correlation more general than entanglement, wherein even a separable state may yield correlation that cannot be emulated by any classical object. Such a general nonclassical correlation is not only intriguing from the fundamental point of view, but it has also been recognized as a resource in a variety of quantum information processing tasks and quantum technology. Here, we propose a characterization of the general quantum correlation in bipartite system in terms of direct laboratory operations using weak measurement with postselection. We define a quantity based on the imaginary part of weak values obtained via weak measurement of a local basis followed by a postselection of another local basis, and an optimization procedure over all possible choices of the two bases. We show that it satisfies certain desirable requirements for a quantifier of general quantum correlations. It may be statistically interpreted as the minimum genuine quantum share of uncertainty. It is a faithful witness of entanglement for general pure states, giving an observable lower bound to a scaled square root of the linear entropy of entanglement. We then suggest an information theoretic interpretation of the general quantum correlation in a multipartite state as the minimum mean absolute error in an optimal estimation of any local measurement basis, based on the outcomes of local projective measurement on the state, in the worst case scenario., Comment: 26 pages

We study the Li interstitial diffusion in pristine and defective ZnO bulk by means of first-principles density functional theory (DFT) coupled with Nudged Elastic Band (NEB) calculations. We consider three types of point defects, i.e., oxygen vacancy (Ovac), Zn vacancy (Znvac) and ZnO vacancy pair (ZnOvac-pair) and investigate their individual effect on the energy barrier of Li interstitial diffusion. Our results predict that Ovac and Znvac lower the Li diffusion energy barrier as compared to the pristine ZnO case. However, we further find that Li interstitial on the other hand may possibly be trapped inside the Znvac subsequently forming the LiZn substitutional type of defect. The similar behavior also observed for Li interstitial in the vicinity of Zn-Ovac_pair though with less change of Li diffusion barriers as compared to the other two cases. Our results indicate that among the three considered defects only Ovac shows possible enhancement of the kinetics of Li diffusion inside ZnO bulk.

One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of quantum mechanics within a general epistemic framework based on an operational scheme of estimation of momentum given positions under epistemic restriction. The epistemic restriction is parameterized by a global-nonseparable random variable on the order of Planck constant, an ontic extension to the separable classical phase space variables. Within the estimation scheme, the canonical quantum laws is reconstructed for a specific estimator and estimation error. In the present work, keeping the Born's quadratic law intact, we construct a class of nonlinear variants of Schr\"odinger equation and generalized Heisenberg uncertainty principle within the estimation scheme by assuming a more general class of estimation errors. The nonlinearity of the Schr\"odinger equation and the deviation from the Heisenberg uncertainty principle thus have a common transparent operational origin in terms of generalizations of estimation errors. We then argue that a broad class of nonlinearities and deviations from Heisenberg uncertainty principle arise from estimation errors violating a plausible inferential-causality principle of estimation independence which is respected by the standard quantum mechanics. This result therefore constrains possible extensions of quantum mechanics, and suggests directions to generalize quantum mechanics which comply with the principle of estimation independence.

One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of quantum mechanics within a general epistemic framework based on an operational scheme of estimation of momentum given positions under epistemic restriction. The epistemic restriction is parameterized by a global-nonseparable random variable on the order of Planck constant, an ontic extension to the separable classical phase space variables. Within the estimation scheme, the canonical quantum laws is reconstructed for a specific estimator and estimation error. In the present work, keeping the Born's quadratic law intact, we construct a class of nonlinear variants of Schr��dinger equation and generalized Heisenberg uncertainty principle within the estimation scheme by assuming a more general class of estimation errors. The nonlinearity of the Schr��dinger equation and the deviation from the Heisenberg uncertainty principle thus have a common transparent operational origin in terms of generalizations of estimation errors. We then argue that a broad class of nonlinearities and deviations from Heisenberg uncertainty principle arise from estimation errors violating a plausible inferential-causality principle of estimation independence which is respected by the standard quantum mechanics. This result therefore constrains possible extensions of quantum mechanics, and suggests directions to generalize quantum mechanics which comply with the principle of estimation independence.