Quantum entanglement of identical particles

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 2, 2003, Pages

  Shi, Yu ^a,b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGED PARTICLES; ELECTRONIC DENSITY OF STATES; FERMIONS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; STATE SPACE METHODS;

DENSITY MATRIX; QUANTUM ENTANGLEMENT; SCHMIDT BASIS;

QUANTUM THEORY;

EID: 0037626046     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. E. Knill, R. Laflamme, and G.J. Milburn, Nature (London) 409, 46 (2001).
2. P. Zanardi, Phys. Rev. A 65, 042101 (2002).
3. D. Loss and D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
4. C.N. Yang, Rev. Mod. Phys. 34, 694 (1962), see Appendix A
5. J. Schliemann, D. Loss, and A.H. MacDonald, Phys. Rev. B 63, 085311 (2002).
6. J. Schlieman et al., Phys. Rev. A 64, 022303 (2001).
7. K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, e-print quant-ph/0203060.
8. R. Paskauskas and L. You, Phys. Rev. A 64, 042310 (2001).
9. Y.S. Li, B. Zeng, X.S. Liu, and G.L. Long, Phys. Rev. A 64, 054302 (2001).
10. †)|0>, where x + y = 1.
11. 3|3>|3>, where at least two of the coefficients are nonzero. Similar problems exist in the discussions on more general cases.
12. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Boston, 1995).
13. Some transformations, e.g., the one appearing in the exact solution of independent boson model, are global canonical transformation leading to a diagonalized Hamiltonian. Some transformations, e.g., that between Bloch basis and Wannier basis, are single-particle basis transformations. Some transformations, e.g., Jordan-Wigner transformation are based on representing the original operators in terms of new operators, which makes the Hamiltonian diagonal and the eigenstates non-entangled. In some cases, the combination of the original particles gives quasiparticles, for example, polaron, polariton, exciton, etc. Some transformations even split the original operators, e.g., the slave boson approach.
14. Relevant mode means that in at least one of those basis states corresponding to nonzero f, the occupation number of this mode is nonzero. The occupation-number state of an irrelevant mode s simply a factor |0> and can be neglected.
15. X. Hu and S. Das Sarma, Phys. Rev. A 61, 062301 (2000).
16. Y. Shi, e-print quant-ph/0204058; e-print cond-mat/0205272.