Phase-space representations of SIC-POVM fiducial states

Marcos Saraceno, 2 Leonardo Ermann, 3 and Cecilia Cormick Departamento de F́ısica Teórica, Comisión Nacional de Enerǵıa Atómica, Buenos Aires, Argentina Escuela de Ciencia y Tecnoloǵıa, Universidad Nacional de San Martin, San Martin, Argentina CONICET, Godoy Cruz 2290 (C1425FQB) CABA, Argentina IFEG, CONICET and Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina (Dated: December 8, 2016)

[1]  Leslie R. Welch Lower bounds on the maximum correlation of signals , 1974 .

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

[3]  A. M. Almeida The Weyl representation in classical and quantum mechanics , 1998 .

[4]  A. Vourdas Phase space methods for finite quantum systems , 1997 .

[5]  G. Zauner,et al.  QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY , 2011 .

[6]  Andreas Klappenecker,et al.  Mutually unbiased bases are complex projective 2-designs , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[7]  Aephraim M. Steinberg,et al.  Experimental characterization of qutrits using symmetric informationally complete positive operator-valued measurements , 2011 .

[8]  Steven T. Flammia On SIC-POVMs in prime dimensions , 2006 .

[9]  Christopher A. Fuchs,et al.  Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States , 2007, Entropy.

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

[11]  Paul Busch,et al.  Informationally complete sets of physical quantities , 1991 .

[12]  Leonhardt,et al.  Discrete Wigner function and quantum-state tomography. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[13]  J. V. Corbett,et al.  About SIC POVMs and discrete Wigner distributions , 2005 .

[14]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[15]  A. Voros,et al.  Chaos-revealing multiplicative representation of quantum eigenstates , 1990 .

[16]  J. Emerson,et al.  Scalable noise estimation with random unitary operators , 2005, quant-ph/0503243.

[17]  V. Bargmann On a Hilbert space of analytic functions and an associated integral transform part I , 1961 .

[18]  K. Życzkowski,et al.  Geometry of Quantum States , 2007 .

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

[20]  A. Voros,et al.  Chaotic Eigenfunctions in Phase Space , 1997, chao-dyn/9711016.

[21]  M. Grassl On SIC-POVMs and MUBs in Dimension 6 , 2004, quant-ph/0406175.

[22]  Masahide Sasaki,et al.  Squeezing quantum information through a classical channel: measuring the "quantumness" of a set of quantum states , 2003, Quantum Inf. Comput..

[23]  C. Beenakker,et al.  Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems , 1996, cond-mat/9604059.

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

[25]  A. J. Scott,et al.  SIC-POVMs: A new computer study , 2009 .

[26]  D. M. Appleby Symmetric informationally complete measurements of arbitrary rank , 2007 .

[27]  The Weyl Representation on the Torus , 1999, quant-ph/9904041.

[28]  A. J. Scott Tight informationally complete quantum measurements , 2006, quant-ph/0604049.

[29]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[30]  D. M. Appleby SIC‐POVMS and MUBS: Geometrical Relationships in Prime Dimension , 2009 .

[31]  Christoph Dankert,et al.  Exact and approximate unitary 2-designs and their application to fidelity estimation , 2009 .

[32]  Quantum computers in phase space , 2002, quant-ph/0204149.

[33]  H. Weyl The Theory Of Groups And Quantum Mechanics , 1931 .