A unified approach to SIC-POVMs and MUBs

A unified approach to (symmetric informationally complete) positive operator valued measures (SIC-POVMs) and mutually unbiased bases (MUBs) is developed. The approach is based on the use of Racah unit tensors for the Wigner-Racah algebra of SU(2) ⊃ U(1). Emphasis is put on similarities and differences between SIC-POVMs and MUBs.

[1]  A. Vourdas.  Galois quantum systems , 2005 .

[2]  Markus Grassl.  Tomography of Quantum States in Small Dimensions , 2005, Electron. Notes Discret. Math..

[3]  Andrew G. Glen,et al.  APPL , 2001 .

[4]  a SU(2) Recipe for Mutually Unbiased Bases , 2006, quant-ph/0601092.

[5]  Stefan Weigert.  Simple Minimal Informationally Complete Measurements for Qudits , 2006 .

[6]  State space structure and entanglement of rotationally invariant spin systems , 2005, quant-ph/0506224.

[7]  W. D. Muynck.  Foundations of Quantum Mechanics, an Empiricist Approach , 2002 .

[8]  Arthur O. Pittenger,et al.  Mutually Unbiased Bases, Generalized Spin Matrices and Separability , 2003 .

[9]  W. Wootters.  Quantum Measurements and Finite Geometry , 2004, quant-ph/0406032.

[10]  Metod Saniga,et al.  Mutually unbiased bases and finite projective planes , 2004 .

[11]  Ingemar Bengtsson,et al.  Mutually Unbiased Bases and the Complementarity Polytope , 2005, Open Syst. Inf. Dyn..

[12]  Joseph M. Renes,et al.  Symmetric informationally complete quantum measurements , 2003, quant-ph/0310075.

[13]  G. Grenet,et al.  On the SU2 unit tensor , 1980 .

[14]  E. B. Davies,et al.  Information and quantum measurement , 1978, IEEE Trans. Inf. Theory.

[15]  J. Schwinger.  UNITARY OPERATOR BASES. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[16]  John T. Lewis,et al.  An operational approach to quantum probability , 1970 .

[17]  D. M. Appleby.  SIC-POVMs and the Extended Clifford Group , 2004 .

[18]  C. Fuchs,et al.  Unknown Quantum States: The Quantum de Finetti Representation , 2001, quant-ph/0104088.

[19]  G. Racah,et al.  Theory of Complex Spectra. IV , 1942 .

[20]  P. Oscar Boykin,et al.  A New Proof for the Existence of Mutually Unbiased Bases , 2002, Algorithmica.

[21]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[22]  D. M. Appleby.  Symmetric informationally complete–positive operator valued measures and the extended Clifford group , 2005 .

[23]  Freeman J. Dyson,et al.  Irreducible Tensorial Sets , 1960 .

[24]  I. D. Ivonovic.  Geometrical description of quantal state determination , 1981 .

[25]  L. Ballentine,et al.  Quantum Theory: Concepts and Methods , 1994 .

[26]  W. Wootters.  A Wigner-function formulation of finite-state quantum mechanics , 1987 .