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
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
摘要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.
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.
FAN Hong-Yi;WANG Tong-Tong;HU Li-Yun. Normally Ordered Bivariate-Normal-Distribution Forms of Two-Mode Mixed States with Entanglement Involved[J]. 中国物理快报, 2008, 25(10): 3539-3542.
FAN Hong-Yi, WANG Tong-Tong, HU Li-Yun. Normally Ordered Bivariate-Normal-Distribution Forms of Two-Mode Mixed States with Entanglement Involved. Chin. Phys. Lett., 2008, 25(10): 3539-3542.
[1]Fan H Y, Lu H L and Fan Y 2006 Ann. Phys. 321480 Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 147 [2]Fan H Y 2001 Chin. Phys. Lett. 18 1301 Fan H Y and Liu N L 1999 Chin. Phys. Lett. 16 625 [3]Fan H Y and Zaidi H R 1987 Phys. Lett. A 124303 Fan H Y 2001 Chin. Phys. Lett. 18 850 [4]Fan H Y and Li H Q 2007 Chin. Phys. Lett. 243322 [5]Fan H Y 2007 Ann. Phys., doi: 10. 1016/j. aop. 2007. 06.09. [6]Fan H Y 2008 Ann. Phys. 323 500 [7]Walls D F and Milburn G J 1994 Quantum Optics(Berlin: Springer) Orszag M 2000 Quantum Optics (Berlin: Springer) Wolfgang P S 2001 Quantum Optics in Phase Space(Berlin: Wiley) Scully M O and Zubairy M S 1997 Quantum Optics(Cambridge: Cambridge University Press) Mandel L and Wolf E 1995 Optical Coherence and QuantumOptics (Cambridge: Cambridge University) D'Ariano G M, Rassetti M G, Katriel J and Solomon A I 1989 Squeezed and Nonclassical Light (New York: Plenum) [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 [9] Glauber R J 1963 Phys. Rev. 130 2529 Glauber R J 1963 Phys. Rev. 131 2766 [10]Fan H Y and Chen H L 2002 Commun. Theor. Phys. 38 297
2008, Vol. 25 
