Fetching the paper…
Reading the bibliography…
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space.
H. Weyl, The Theory of Groups and Quantum Mechanics, Methuen & co. ltd., London, 1931, translated from the second (revised) German edition by H. P. Robertson
1931
Earlier work this paper cites.
W. Ljunggren, Noen setninger om ubestemte likninger av formen ( x n − 1 ) / ( x − 1 ) = y q (x^{n}-1)/(x-1)=y^{q} , Norsk. Mat. Tidsskr. 25 (1943) 17–20
1943
Earlier work this paper cites.
B. Huppert, Zweifach transitive, auflösbare Permutationsgruppen, Mathematische Zeitschrift 68 (1) (1957) 126–150
1957
Earlier work this paper cites.
B. Bolt, T. G. Room, G. E. Wall, On the Clifford collineation, transform and similarity groups. I., J. Austral. Math. Soc. 2 (1961) 60–79
1961
Earlier work this paper cites.
B. Bolt, T. G. Room, G. E. Wall, On the Clifford collineation, transform and similarity groups. II., J. Austral. Math. Soc. 2 (1961) 80–96
1961
Earlier work this paper cites.
E. Weiss, Algebraic Number Theory, McGraw-Hill Book Company, Inc., New York, 1963
1963
Earlier work this paper cites.
W. M. Kantor, k k -homogeneous groups, Mathematische Zeitschrift 124 (4) (1972) 261–265
1972
Earlier work this paper cites.
A. O. Morris, Projective representations of Abelian groups, J. London Math. Soc. s2-7 (2) (1973) 235–238
1973
Earlier work this paper cites.
C. Hering, Transitive linear groups and linear groups which contain irreducible subgroups of prime order, Geom. Dedicata 2 (4) (1974) 425–460
1974
Earlier work this paper cites.
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, An ATLAS of Finite Groups, Oxford University Press, Oxford, 1985
1985
Earlier work this paper cites.
C. Hering, Transitive linear groups and linear groups which contain irreducible subgroups of prime order, II, J. Algebra 93 (1) (1985) 151–164
1985
Earlier work this paper cites.
W. K. Wootters, A Wigner-function formulation of finite-state quantum-mechanics, Ann. Phys. 176 (1) (1987) 1–21
1987
Earlier work this paper cites.
D. E. Taylor, The geometry of the classical groups, Vol. 9 of Sigma Series in Pure Mathematics, Heldermann Verlag, 1992
1992
Earlier work this paper cites.
P. Ribenboim, Catalan’s Conjecture: Are 8 and 9 the Only Consecutive Powers?, Academic Press, 1994
1994
Earlier work this paper cites.
J. D. Dixon, B. Mortimer, Permutation Groups, Vol. 163 of Graduate Texts in Mathematics, Springer, New York, 1996
1996
Earlier work this paper cites.
D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. thesis, California Institute of Technology, available at http://arxiv.org/abs/quant-ph/9705052 (1997)
1997
Earlier work this paper cites.
S. G. Hoggar, 64 lines from a quaternionic polytope, Geom. Dedicata 69 (1998) 287
1998
Earlier work this paper cites.
P. J. Cameron, Permutation Groups, Vol. 45 of London Mathematical Society Student Texts, Cambridge University Press, Cambridge, UK, 1999
1999
Earlier work this paper cites.
C. A. Fuchs, M. Sasaki, Squeezing quantum information through a classical channel: Measuring the “quantumness” of a set of quantum states, Quant. Inf. Comput. 3 (5) (2003) 377–404
2003
Earlier work this paper cites.
J. M. Renes, R. Blume-Kohout, A. J. Scott, C. M. Caves, Symmetric informationally complete quantum measurements, J. Math. Phys. 45 (2004) 2171, supplementary information including the fiducial kets available at http://www.cquic.org/papers/reports/
2004
Earlier work this paper cites.
J. M. Renes, Frames, designs, and spherical codes in quantum information theory, Ph.D. thesis, The University of New Mexico (2004)
2004
Cited alongside, same era.
B.-G. Englert, D. Kaszlikowski, H. K. Ng, W. K. Chua, J. Řeháček, J. Anders, Efficient and robust quantum key distribution with minimal state tomography, available at http://arxiv.org/abs/quant-ph/0412075 (2004)
2004
Cited alongside, same era.
H. Kurzweil, B. Stellmacher, The Theory of Finite Groups: An Introduction, Springer, New York, 2004
2004
Cited alongside, same era.
J. M. Renes, Equiangular spherical codes in quantum cryptography, Quantum Inf. Comput. 5 (2005) 81
2005
Cited alongside, same era.
D. M. Appleby, Symmetric informationally complete-positive operator valued measures and the extended Clifford group, J. Math. Phys. 46 (2005) 052107
2005
Cited alongside, same era.
H. Zhu, B.-G. Englert, Quantum state tomography with fully symmetric measurements and product measurements, Phys. Rev. A 84 (2011) 022327
2011
Later among the works it cites.
D. M. Appleby, S. T. Flammia, C. A. Fuchs, The Lie algebraic significance of symmetric informationally complete measurements, J. Math. Phys. 52 (2011) 022202
2011
Later among the works it cites.
H. Zhu, Quantum state estimation and symmetric informationally complete POMs, Ph.D. thesis, National University of Singapore, available at http://scholarbank.nus.edu.sg/bitstream/handle/10635/35247/ZhuHJthesis.pdf (2012)
2012
Later among the works it cites.
D. Petz, L. Ruppert, Efficient quantum tomography needs complementary and symmetric measurements, Rep. Math. Phys. 69 (2) (2012) 161–177
2012
Later among the works it cites.
C. A. Fuchs, R. Schack, Quantum-Bayesian coherence, Rev. Mod. Phys. 85 (2013) 1693–1715
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
I. Bengtsson, K. Życzkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, Cambridge University Press, Cambridge, UK, 2006
2006
Cited alongside, same era.
A. J. Scott, Tight informationally complete quantum measurements, J. Phys. A: Math. Gen. 39 (2006) 13507
2006
Cited alongside, same era.
S. D. Howard, A. R. Calderbank, W. Moran, The finite Heisenberg-Weyl groups in radar and communications, EURASIP J. Appl. Signal Processing 2006 (2006) 85685
2006
Cited alongside, same era.
L. Hughston, d = 3 d=3 SIC-POVMs and elliptic curves, Perimeter Institute, seminar talk, available online at http://pirsa.org/07100040/ (2007)
2007
Cited alongside, same era.
R. B. Ash, Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates, Dover, New York, 2007
2007
Cited alongside, same era.
Y. Bugeaud, P. Mihăilescu, On the Nagell-Ljunggren equation ( x n − 1 ) / ( x − 1 ) = y q (x^{n}-1)/(x-1)=y^{q} , Math. Scand. 101 (2007) 177–183
2007
Cited alongside, same era.
T. Durt, C. Kurtsiefer, A. Lamas-Linares, A. Ling, Wigner tomography of two-qubit states and quantum cryptography, Phys. Rev. A 78 (2008) 042338
2008
Cited alongside, same era.
2013
Later among the works it cites.
G. N. M. Tabia, D. M. Appleby, Exploring the geometry of qutrit state space using symmetric informationally complete probabilities, Phys. Rev. A 88 (2013) 012131
2013
Later among the works it cites.
H. B. Dang, K. Blanchfield, I. Bengtsson, D. M. Appleby, Linear dependencies in Weyl–Heisenberg orbits, Quantum Inf. Process. 12 (11) (2013) 3449–3475
2013
Later among the works it cites.
H. Zhu, Quantum state estimation with informationally overcomplete measurements, Phys. Rev. A 90 (2014) 012115
2014
Closest in time.
H. Zhu, Tomographic and Lie algebraic significance of generalized symmetric informationally complete measurements, Phys. Rev. A 90 (2014) 032309
2014
Closest in time.
D. M. Appleby, C. A. Fuchs, H. Zhu, unpublished (2014)
2014
Closest in time.
L. Hughston, S. Salamon, Surveying points in the complex projective plane (2014) · 2014
Closest in time.
D. M. Appleby, C. A. Fuchs, H. Zhu, Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem, Quantum Inf. Comput. 15 (1-2) (2015) 61–94
2015
Closest in time.
H. Zhu, Permutation symmetry determines the discrete Wigner function (2015) · 2015
Closest in time.
H. Zhu, Mutually unbiased bases as minimal Clifford covariant 2-designs, Phys. Rev. A 91 (2015) 060301
2015
Closest in time.
H. Zhu, in preparation (2015)
2015
Closest in time.
H. Zhu, Sharply covariant mutually unbiased bases (2015) · 2015
Closest in time.
H. Zhu, Nonexistence of sharply covariant mutually unbiased bases in odd prime dimensions, to appear in Phys. Rev. A. (2015) · 2015
Closest in time.
C. Bessenrodt, H. N. Nguyen, J. B. Olsson, H. P. Tong-Viet, Complex group algebras of the double covers of the symmetric and alternating groups, Algebra & Number Theory 9 (3) (2015) 601–628
2015
Closest in time.
P. H. Tiep, A. E. Zalesskii, Minimal characters of the finite classical groups, Commun. Algebra 24 (6) (1996) 2093–2167
2093
Closest in time.