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Chinese Physics Letters

Normally Ordered Bivariate-Normal-Distribution Forms of Two-Mode Mixed States with Entanglement Involved

范洪义, 王彤彤, 胡利云

Published Jan 1, 2008• 0 citations
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Abstract

在我们表明了的操作员的一个订的产品以内基于集成的技术那个单个模式的混合状态的密度矩阵能被重做进通常订的 Gaussian 形式[下巴。Phys。Lett。24 (2007 ) 3322 ] 。这里，我们采用在类似的转变下面订不变性到有包含的纠纷的一些二模式的混合状态能通常被放进的表演的 Weyl 在 bivariate 正常分发的征订表也并且它的边缘的分布能被分析。这样，量统计的密度操作员能类似于数学统计，并且变化的计算能被简化。[从作者抽象]

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在我们表明了的操作员的一个订的产品以内基于集成的技术那个单个模式的混合状态的密度矩阵能被重做进通常订的 Gaussian 形式[下巴。Phys。Lett。24 (2007 ) 3322 ] 。这里，我们采用在类似的转变下面订不变性到有包含的纠纷的一些二模式的混合状态能通常被放进的表演的 Weyl 在 bivariate 正常分发的征订表也并且它的边缘的分布能被分析。这样，量统计的密度操作员能类似于数学统计，并且变化的计算能被简化。[从作者抽象]
Based on the technique of integration within an ordered product of operators we have demonstrated that single-mode mixed states' density matrices can be recast into the normally ordered Gaussian forms [Chin. Phys. Lett. 24 (2007) 3322]. Here we employ the Weyl ordering invariance under similar transformations to show that some two-mode mixed states with entanglement involved can be put into normally ordered form in the bivariate normal distribution too and its marginal distributions can be analysed. In this way, density operators of quantum statistics can be analogous to mathematical statistics, and calculation of variances can be simplified.
Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states (such as the coordinate eigenstate, the momentum eigenstate and the coherent state) into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.