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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Husimi Q representation ： ウィキペディア英語版 Husimi Q representation The Husimi Q representation, introduced by in 1940,〔Kôdi Husimi (1940). "Some Formal Properties of the Density Matrix", ''Proc. Phys. Math. Soc. Jpn.'' 22: 264-314 .〕 is a quasiprobability distribution commonly used in quantum mechanics〔 〕 to represent the phase space distribution of a quantum state such as light in the phase space formulation.〔Ulf Leonhardt (1997). ''Measuring the Quantum State of Light'', Cambridge Studies in Modern Optics. ISBN 0521497302 , ISBN 978-0521497305.〕 It is used in the field of quantum optics〔H. J. Carmichael (2002). ''Statistical Methods in Quantum Optics I: Master Equations and Fokker-Planck Equations'', Springer-Verlag. ISBN 978-3-540-54882-9〕 and particularly for tomographic purposes. It is also applied in the study of quantum effects in superconductors. ==Definition and properties== The Husimi Q distribution (called Q-function in the context of quantum optics) is one of the simplest distributions of quasiprobability in phase space. It is constructed in such a way that observables written in ''anti''-normal order follow the optical equivalence theorem. This means that it is essentially the density matrix put into normal order. This makes it relatively easy to calculate compared to other quasiprobability distributions through the formula : $Q(\backslash alpha)=\backslash frac\backslash langle\backslash alpha|\backslash hat|\backslash alpha\backslash rangle,$ which is effectively a trace of the density matrix over the basis of coherent states $\backslash$. It produces a pictorial representation of the state ''ρ'' to illustrate several of its mathematical properties.〔Cosmas K. Zachos, David B. Fairlie, and Thomas L. Curtright (2005). ''Quantum Mechanics in Phase Space'', (World Scientific, Singapore) ISBN 978-981-238-384-6 ().〕 Its relative ease of calculation is related to its smoothness compared to other quasiprobability distributions. In fact, it can be understood as the Weierstrass transform of the Wigner quasiprobability distribution, i.e. a smoothing by a Gaussian filter, :$Q(\backslash alpha)=\; \backslash frac\; \backslash int\; W(\backslash beta)\; e^\; \backslash ,\; d^2\backslash beta.$ Such Gauss transforms being essentially invertible in the Fourier domain via the convolution theorem, ''Q'' provides an equivalent description of quantum mechanics in phase space to that furnished by the Wigner distribution. Alternatively, one can compute the Husimi Q distribution by taking the Segal–Bargmann transform of the wave function and then computing the associated probability density. ''Q'' is normalized to unity, : $\backslash int\; Q(\backslash alpha)\backslash ,d\backslash alpha^2\; =\; 1$ and is ''non-negative definite'' and ''bounded'': : $0\; \backslash leq\; Q(\backslash alpha)\; \backslash leq\; \backslash frac.$ Despite the fact that is non-negative definite and bounded like a standard joint probability distribution, this similarity may be misleading, because different coherent states are not orthogonal. Two different points do not represent disjoint physical contingencies; thus, ''Q(α)'' does ''not represent the probability of mutually exclusive states'', as needed in the third axiom of probability theory. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Husimi Q representation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.