Chin. Phys. Lett.  2008, Vol. 25 Issue (10): 3539-3542    DOI:
Original Articles |
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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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.
Keywords: 03.65.-w      63.20.-e      42.50.-p     
Received: 11 March 2008      Published: 26 September 2008
PACS:  03.65.-w (Quantum mechanics)  
  63.20.-e (Phonons in crystal lattices)  
  42.50.-p (Quantum optics)  
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Articles by authors
FAN Hong-Yi
WANG Tong-Tong
HU Li-Yun
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[6]Fan H Y 2008 Ann. Phys. 323 500
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[8]Buzek V 1990 J. Mod. Opt. 37 303 Loudon R and Knight P L 1987 J. Mod. Opt. 34 709 Dodonov V V 2002 J. Opt. B: Quant. Semiclass.Opt. 4 R1
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[10]Fan H Y and Chen H L 2002 Commun. Theor. Phys. 38 297
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