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Normally Ordered Bivariate-Normal-Distribution Forms of Two-Mode Mixed States with Entanglement Involved |
FAN Hong-Yi1,2, WANG Tong-Tong1, HU Li-Yun2 |
1Department of Material Science and Engineering, University of Science and Technology of China, Hefei 2300262Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 |
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Cite this article: |
FAN Hong-Yi, WANG Tong-Tong, HU Li-Yun 2008 Chin. Phys. Lett. 25 3539-3542 |
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Abstract 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.
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Keywords:
03.65.-w
63.20.-e
42.50.-p
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Received: 11 March 2008
Published: 26 September 2008
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