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Nonclassical light states are important for both conceptual and practical reasons: they are basic ingredients in testing and exploring quantum foundations, and are crucial resources in quantum technologies. Various useful criteria have been developed to detect nonclassicality in the literature, and several meaningful measures of nonclassicality have been introduced and measured experimentally. In this work, by use of a non-Hermitian generalization of the Wigner-Yanase-Dyson skew information and playing with operator ordering in evaluating average photon number, we develop a novel family of criteria for detecting nonclassicality of light based on Lieb's concavity, which is a deep and powerful result concerning interaction between quantum states and observables. We elucidate the information-theoretic as well as the physical meaning of the criteria, and illustrate their effectiveness in capturing and quantifying nonclassicality of various important light states. 相似文献
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We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming. 相似文献
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Lu Chuanrong 《数学年刊B辑(英文版)》1997,18(1):71-78
Let $\{\xi_{\bold t}, {\bold t}
\in {\bold Z}^d\}$ be a nonuniform $\varphi$-mixing strictly stationary
real random field with
$E\xi_{\bold 0}=0, E|\xi_{\bold 0}|^{2+\delta}<\infty$ for some
$0<\delta<1$. A sufficient
condition is given for the sequence of partial sum set-indexed process
$\{Z_n(A),\ A\in \Cal A\}$ to converge to Brownian motion. By a direct
calculation, the author shows
that the result holds for a more general class of set index ${\Cal A}$, where
${\Cal A}$ is assumed only to have the metric entropy exponent $r, 0相似文献
7.
We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice. 相似文献
8.
R. S. Martynov Yu. M. Nechepurenko 《Computational Mathematics and Mathematical Physics》2006,46(7):1155-1167
For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented. 相似文献
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In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $. 相似文献