Quantum-state tomography for spin-l systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 69, Issue 4, 2004, Pages

  Hofmann, Holger F ^a   Takeuchi, Shigeki ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COHERENT LIGHT; CORRELATION METHODS; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PHOTONS; PROBABILITY DISTRIBUTIONS; RELAXATION PROCESSES; STATISTICS; TOMOGRAPHY; VECTORS;

HERMITIAN OPERATORS; NEUMANN MEASUREMENTS; QUANTUM-STATE TOMOGRAPHY; STOKES VECTORS;

QUANTUM THEORY;

EID: 2942670650     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.69.042108     Document Type: Article

References (16)

1. T. Tsegaye, J. Soderholm, M. Atature, A. Trifonov, G. Bjork, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 85, 5013 (2000).
2. A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, Phys. Rev. A 64, 041803(R) (2001).
3. A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, Nature (London) 412, 887 (2001).
4. J. C. Howell, A. Lamas-Linares, and D. Bouwmeester, Phys. Rev. Lett. 88, 030401 (2002).
5. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
6. A. Vaziri, G. Weihs, and A. Zeilinger, Phys. Rev. Lett. 89, 240401 (2002).
7. A. G. White, D. F. V. James, P. H. Eberhard, and P. G. Kwiat, Phys. Rev. Lett. 83, 3103 (1999).
8. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 66, 052312 (2001).
9. R. T. Thew, K. Nemoto, A. G. White, and W. J. Munro, Phys. Rev. A 66, 012303 (2002).
10. G. Klose, G. Smith, and P. S. Jessen, Phys. Rev. Lett. 86, 4721 (2001).
11. i in Eq. (2).
12. It has recently come to our attention that a particular choice of 4l+1 measurement directions was proposed as early as 1968 by R. G. Newton and B.-L. Young, Ann. Phys. (N.Y.) 49, 393 (1968). The results in this paper show that 4l+1 measurement directions are also sufficient for quantum tomography. However, Newton and Young suggested that a better choice of directions could reduce the number of measurement directions needed. Our results show that this is in fact impossible.
13. F. T. Hioe and J. H. Eberly, Phys. Rev. Lett. 47, 838 (1981).
14. G. Mahler and V. A. Weberruß, Quantum Networks (Springer, Berlin, 1998), p. 44.
15. H. F. Hofmann, Phys. Rev. A 68, 034307 (2003).
16. 2l〉 itself is a consequence of the fact that the discreteness of the quantized eigenvalues makes a higher resolution unnecessary.