New equation for deriving pure state density operators by Weyl correspondence and Wigner operator

doi:10.1088/1674-1056/19/2/020303

Abstract By virtue of the completeness of Wigner operator and Weyl correspondence we construct a general equation for deriving pure state density operators. Several important examples are considered as the applications of this equation, which shows that our approach is effective and convenient for deducing these entangled state representations.

Keywords: density operator Weyl ordering Wigner operator quantum mechanical eigenstate

Received: 26 May 2009
Revised: 03 July 2009
Accepted manuscript online:

PACS:	03.65.Ud	(Entanglement and quantum nonlocality)
	03.65.Fd	(Algebraic methods)
	02.10.Ud	(Linear algebra)
	02.30.Tb	(Operator theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10874174 and 90203002).

Cite this article:

Xu Ye-Jun(许业军), Fan Hong-Yi(范洪义), and Liu Qiu-Yu(刘秋宇) New equation for deriving pure state density operators by Weyl correspondence and Wigner operator 2010 Chin. Phys. B 19 020303

[1]	Wely H 1932 Z. Phys. 46 1
[2]	Vogel K and Risken H 1989 Phys. Rev. A 40 2847
[3]	Agarwal G S and Wolf E 1970 Phys. Rev. D 22161
[3a]	Agarwal G S and Wolf E 1970 Phys. Rev. D 2 2187
[3b]	Agarwal G S and Wolf E 1970 Phys. Rev. D 2 2206
[4]	Walls D F and Milburn G 1994 Quantum Optics (Berlin: Springer-Verlag)
[5]	Smithey D T, Beck M and Raymer M G 1993 Phys. Rev. Lett. 70 1244
[6]	Wu H J and Fan H Y 1997 Mod. Phys. Lett. B 11544
[6a]	Fan H Y 2001 J. Opt. B: Quantum Semiclass. Opt. 3 388
[6b]	Fan H Y and Sun Z H 2000 Phys. Lett. A 272219
[7]	Ahn D, Lee H J and Hwang S W 2003 Phys. Rev. A 67 032309
[7a]	Ahn D, Lee H J and Hwang S W 2003 Phys. Rev. A 61 052310
[8]	Ekert A and Josza R 1996 Rev. Mod. Phys. 68 733
[9]	DiVincenzo D P 1995 Science 2 70 255
[10]	Bernett C H, Brassard G and Crepeau C 1993 Phys. Rev. Lett. 701895
[11]	Fan H Y and Klauder J R 1994 Phys. Rev. A 49704
[11a]	Fan H Y and Fan Y 1996 Phys. Rev. A 54958
[11b]	Fan H Yand Chen B Z 1996 Phys. Rev. A 5 3 2948
[12]	Preskill J 1998 Quantum Information and Computation,Lecture Notes for Physics(Pasadena: California Institute ofTechnology) p229
[13]	Smithey D T, Beck M, Raymer M G and Faridani A 1993 Phys. Rev. Lett. 70 1244
[14]	Wigner E P 1932 Phys. Rev. 40 749
[15]	Jiang N Q 2005 Phys. Lett. A 339 255
[16]	Fan H Y, Zaidi H R and Klauder J R 1987 Phys. Rev. D 35 1831
[16a]	FanH Y 1990 Phys. Rev. A 41 1526
[17]	Fan H Y and Hu L Y 2009 Chin. Phys. B 18902
[17a]	Fan H Y and Hu L Y 2009 Chin. Phys. B 18 1061
[17b]	Fan H Yand Hu L Y 2009 Chin. Phys. B 18 611
[17c]	Fan H Y and Hu L Y2008 Chin. Phys. B 17 1640
[17d]	Fan H Y and Hu L Y 2008 Chin. Phys. B 17 697
[18]	Fan H Y and Zaidi H R 1987 Phys. Lett. A 124 303
[29]	Weyl H 1927 Z. Phys. 46 1
[20]	Fan H Y 1992 J. Phys. A 25 3443
[21]	Ekert A and Josza R 1996 Rev. Mod. Phys. 68 733
[22]	DiVincenzo D P 1995 Science 2 70 255
[23]	Fuchs C A, Gisin N, Griffiths R B, Niu C S and Peres A 1997 Phys. Rev. A 56 1163
[24]	Fan H Y and Klauder J R 1994 Phys. Rev. A 49704
[24a]	Fan H Y and Fan Y 1996 Phys. Rev. A 54958
[24b]	Fan H Yand Chen B Z 1996 Phys. Rev. A 5 3 2948
[24c]	Fan H Y and Hu LY 2009 Chin. Phys. B 18 918
[25]	Milburn G J and Braunstein S L 1999 Phys. Rev. A 60 937
[26]	Fan H Y 2001 Phys. Lett. A 286 81
[26a]	Fan H Y andYe X 1995 Phys. Rev. A 51 3343
[26b]	Fan H Y 2002 Phys.Rev. A 65 064102
[26c]	Fan H Y 2002 Phys. Lett. A 294 253

[1]	Evolution of quantum states via Weyl expansion in dissipative channel Li-Yun Hu(胡利云), Zhi-Ming Rao(饶志明), Qing-Qiang Kuang(况庆强). Chin. Phys. B, 2019, 28(8): 084206.
[2]	Gazeau-Klauder coherent states examined from the viewpoint of diagonal ordering operation technique Dušan Popov, Romeo Negrea, Miodrag Popov. Chin. Phys. B, 2016, 25(7): 070301.
[3]	Mutual transformations between the P–Q,Q–P, and generalized Weyl ordering of operators Xu Xing-Lei (徐兴磊), Li Hong-Qi (李洪奇), Fan Hong-Yi (范洪义). Chin. Phys. B, 2014, 23(3): 030305.
[4]	A generalized Weyl–Wigner quantization scheme unifying P–Q and Q–P ordering and Weyl ordering of operators Wang Ji-Suo(王继锁), Fan Hong-Yi(范洪义), and Meng Xiang-Guo(孟祥国) . Chin. Phys. B, 2012, 21(6): 064204.
[5]	The Fourier slice transformation of the Wigner operator and the quantum tomogram of the density operator Wang Tong-Tong(王彤彤) and Fan Hong-Yi(范洪义) . Chin. Phys. B, 2012, 21(3): 034203.
[6]	A new bipartite entangled state describing the parametric down-conversion process and its applications in quantum optics Meng Xiang-Guo (孟祥国), Wang Ji-Suo (王继锁), Zhang Xiao-Yan (张晓燕). Chin. Phys. B, 2012, 21(10): 100305.
[7]	A new approach to obtaining positive-definite Wigner operator for two entangled particles with different masses Fan Hong-Yi(范洪义), Xu Xue-Xiang(徐学翔), Yuan Hong-Chun(袁洪春), Wang Shuai(王帅), Wang Zhen(王震), Xu Peng(许朋), and Jiang Nian-Quan(姜年权) . Chin. Phys. B, 2011, 20(7): 070301.
[8]	New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case Fan Hong-Yi (范洪义), Yuan Hong-Chun (袁洪春). Chin. Phys. B, 2010, 19(7): 070301.
[9]	The s-parameterized Weyl－Wigner correspondence in the entangled form and its applications Fan Hong-Yi(范洪义), Hu Li-Yun(胡利云), and Yuan Hong-Chun(袁洪春). Chin. Phys. B, 2010, 19(6): 060305.
[10]	Unifying the theory of integration within normal-, Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators Fan Hong-Yi(范洪义). Chin. Phys. B, 2010, 19(5): 050303.
[11]	New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering Fan Hong-Yi(范洪义). Chin. Phys. B, 2010, 19(4): 040305.
[12]	Radon transforms of the Wigner operator on hyperplanes Chen Jun-Hua(陈俊华) and Fan Hong-Yi(范洪义). Chin. Phys. B, 2009, 18(9): 3714-3718.
[13]	Wigner function of the thermo number states Hu Li-Yun(胡利云) and Fan Hong-Yi(范洪义). Chin. Phys. B, 2009, 18(3): 902-909.
[14]	New approach for deriving density operator for describing continuum photodetection process Fan Hong-Yi(范洪义) and Hu Li-Yun(胡利云). Chin. Phys. B, 2009, 18(3): 1061-1064.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

New equation for deriving pure state density operators by Weyl correspondence and Wigner operator

Cite this article:

Online attention