Search

Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in KD (Kirkwood-Dirac) quasiprobability distribution, the distinctive quantum mechanical feature of noncommutativity which underlies many nonclassical phenomena, manifests in the nonreal values and/or the negative values of the real part. Here, we develop a faithful quantifier of quantum coherence based on the KD nonclassicality which captures simultaneously the nonreality and the negativity of the KD quasiprobability. The KD-nonclassicality coherence thus defined, is upper bounded by the uncertainty of the outcomes of measurement described by a rank-1 orthogonal PVM (projection-valued measure) corresponding to the incoherent orthonormal basis which is quantified by the Tsallis $\frac{1}{2}$-entropy. Moreover, they are identical for pure states so that the KD-nonclassicallity coherence for pure state admits a simple closed expression in terms of measurement probabilities. We then use the Maassen-Uffink uncertainty relation for min-entropy and max-entropy to obtain a lower bound for the KD-nonclassicality coherence of a pure state in terms of optimal guessing probability in measurement described by a PVM noncommuting with the incoherent orthonormal basis. We also derive a trade-off relation for the KD-noncassicality coherences of a pure state relative to a pair of noncommuting orthonormal bases with a state-independent lower bound. Finally, we sketch a variational scheme for a direct estimation of the KD-nonclassicality coherence based on weak value measurement and thereby discuss its relation with quantum contextuality., Comment: 36 pages, 2 figures, accepted for publication in J. Phys. A: Math. Theor

Quantum coherence as an asymmetry relative to a translation group generated by a Hermitian operator, is a necessary resource for the quantum parameter estimation. On the other hand, the sensitivity of the parameter estimation is known to be related to the imaginary part of the weak value of the Hermitian operator generating the unitary imprinting of the parameter being estimated. This naturally suggests a question if one can use the imaginary part of the weak value to characterize the coherence as asymmetry. In this work, we show that the average absolute imaginary part of the weak value of the generator of the translation group, maximized over all possible projective measurement bases, can be used to quantify the coherence as asymmetry relative to the translation group, satisfying certain desirable requirements. We argue that the quantifier of coherence so defined, called TC (translationally-covariant) w-coherence, can be obtained experimentally using a hybrid quantum-classical circuit via the estimation of weak value combined with a classical optimization procedure. We obtain upper bounds of the TC w-coherence in terms of the quantum standard deviation, quantum Fisher information, and the imaginary part of the Kirkwood-Dirac quasiprobability. We further obtain a lower bound and derive a relation between the TC w-coherences relative to two generators of translation group taking a form analogous to the Kennard-Weyl-Robertson uncertainty relation., Comment: 31 pages, no figures

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.