An Entanglement Criterion for States in Infinite Dimensional Bipartite Quantum Systems

Yinzhu Wang, Danxia Wang

Department of Mathematics, Taiyuan University of Science and Technology, Taiyuan, China.
School of Mathematics, Taiyuan University of Technology, Taiyuan, China.

DOI: 10.4236/jqis.2012.23013                

Abstract

In this paper, an entanglement criterion for states in infinite dimensional bipartite quantum systems is presented. We generalize some of separability criterion that was recently introduced by Wu and Anandan in (Phys. Lett. A, 2002, 297, 4-8) to infinite dimensional bipartite quantum systems. In addition, we give an example aimed to illustrate the application of the theorem.

Keywords

Entanglement Criterion; Infinite Dimensional Quantum Systems; Bochner Integral Representation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. A. Nielsen and I. L. Chang, “Quantum Computation and Quantum Information,” Cambridge University press, Cambridge, 2000.
[2]	A. Peres, “Separability Criterion for Density Matrices,” Physical Review Letters, Vol. 77, No. 8, 1996, pp. 1413-1418. doi:10.1103/PhysRevLett.77.1413
[3]	K. Zyczkowski, P. Horodecki, A. Sanpera, et al., “Volume of the Set of Separable States,” Physical Review A, Vol. 58, No. 2, 1998, pp. 883-896. doi:10.1103/PhysRevA.58.883
[4]	M. Horodecki, P. Horodecki and R. Horodecki, “Separability of Mixed States: Necessary and Sufficient Conditions,” Physical Review A, Vol. 223, No. 1-2, 1996, pp. 1-14. doi:10.1016/S0375-9601(96)00706-2
[5]	M. Horodecki and P. Horodecki, “Reduction Criterion of Separability and Limits for a Class of Distillation Protocols,” Physical Review A, Vol. 59, No. 6, 1999, pp. 4206-4216. doi:10.1103/PhysRevA.59.4206
[6]	M. A. Nielsen and J. Kempe, “Separable States Are More Disordered Globally than Locally,” Physical Review Letters, Vol. 86, No. 22, 2001, pp. 5184-5187. doi:10.1103/PhysRevLett.86.5184
[7]	O. Rudolph, “Further Results on the Cross Norm Criterion for Separability,” Quantum Information Processing, Vol. 4, No. 3, 2005, pp. 219-239. doi:10.1007/s11128-005-5664-1
[8]	R. F. Werner, “Quantum States with Einstein-Podolsky-Rosen Correlations Admitting a Hidden-Variable Model,” Physical Review A, Vol. 40, No. 8, 1989, pp. 4277-4281. doi:10.1103/PhysRevA.40.4277
[9]	X. L. Su, X. J. Jia, C. D. Xie, et al., “Generation of GHZ-Like and Duster-Like Quadripripartite Entangled States for Continuous Variable Using a Set of Quadrature Squeezed States,” Science in China Series G: Physics Mechanics and Astronomy, Vol. 51, No. 1, 2008, pp. 1-13. doi:10.1007/s11433-008-0004-y
[10]	S. J. Wu and J. Anandan, “Some Aspects of Separability,” Physical Review A, Vol. 297, No. 1-2, 2002, pp. 4-8. doi:10.1016/S0375-9601(02)00279-7
[11]	A. S. Holevo, M. E. Shirokov and R. F. Werner, “Separability and Entanglement-Breaking in Infinite Dimensionals,” Russian Math Surveys, Vol. 60, No. 2, 2005, pp. 1-12.