Fetching the paper…
Reading the bibliography…
We show that weighted unitary 2-designs define optimal measurements on the system-ancilla output state for ancilla-assisted process tomography of unital quantum channels.
K. Kraus, “General state changes in quantum theory,” Ann. Phys. 64
1971
Earlier work this paper cites.
A. Jamiołkowski, “Linear transformations which preserve trace and positive semidefiniteness of operators,” Rep. Math. Phys. 3
1972
Earlier work this paper cites.
L. R. Welch, “Lower bounds on the maximum cross correlation of signals,” IEEE Trans. Inf. Theory 20
1974
Earlier work this paper cites.
G. N. Salihov, “Cubature formulas for a hypersphere that are invariant with respect to the group of the regular 600-face,” (Russian) Dokl. Akad. Nauk SSSR 223
1975
Earlier work this paper cites.
M.-D. Choi, “Completely positive linear maps on complex matrices,” Lin. Alg. Appl. 10
1975
Earlier work this paper cites.
P. Delsarte, J. M. Goethals and J. J. Seidel, “Spherical codes and designs,” Geom. Dedicata 6
1977
Earlier work this paper cites.
E. Prugovec̆ki, “Information-theoretic aspects of quantum measurement,” Int. J. Theor. Phys. 16
1977
Earlier work this paper cites.
E. Bannai and R. Damerell, “Tight spherical designs I,” J. Math. Soc. Japan 31
1979
Earlier work this paper cites.
E. Bannai and R. Damerell, “Tight spherical designs II,” J. London Math. Soc. (2) 21
1980
Earlier work this paper cites.
A. Neumaier, “Combinatorial configurations in terms of distances,” Dept. of Mathematics Memorandum 81-09 (Eindhoven University of Technology, 1981)
1981
Earlier work this paper cites.
I. D. Ivanović, “Geometrical description of quantal state determination,” J. Phys. A 14
1981
Earlier work this paper cites.
S. G. Hoggar, “ t t -designs in projective spaces,” Europ. J. Combin. 3
1982
Earlier work this paper cites.
K. Kraus, States, Effects and Operations
1983
Earlier work this paper cites.
P. D. Seymour and T. Zaslavsky, “Averaging sets: a generalization of mean values and spherical designs,” Adv. Math. 52
1984
Earlier work this paper cites.
I. Daubechies, A. Grossmann and Y. Meyer, “Painless nonorthogonal expansions,” J. Math. Phys. 27
1986
Earlier work this paper cites.
W. K. Wootters and B. D. Fields, “Optimal state-determination by mutually unbiased measurements,” Ann. Phys. 191
1989
Earlier work this paper cites.
P. Busch, “Informationally complete sets of physical quantities,” Int. J. Theor. Phys. 30
1991
Earlier work this paper cites.
K. R. W. Jones, “Principles of quantum inference,” Ann. Phys. 207
1991
Earlier work this paper cites.
L. J. Landau and R. F. Streater, “On Birkoff’s theorem for doubly stochastic completely positive maps of matrix algebras,” Lin. Alg. Appl. 193
1993
Earlier work this paper cites.
P. Diaconis and M. Shahshahani, “On the eigenvalues of random matrices,” J. Appl. Prob. 31
1994
Cited alongside, same era.
R. H. Hardin and N. J. A. Sloane, “Expressing ( a 2 + b 2 + c 2 + d 2 ) 3 (a^{2}+b^{2}+c^{2}+d^{2})^{3} as a sum of 23 sixth powers,” J. Combin. Theory A 68
1994
Cited alongside, same era.
B. Reznick, “Some constructions of spherical 5-designs,” Lin. Alg. Appl. 226-228
1995
Cited alongside, same era.
P. Busch, P. J. Lahti and P. Mittelstaedt, The Quantum Theory of Measurement
1996
Cited alongside, same era.
Z. Hradil, “Quantum-state estimation,” Phys. Rev. A 55
1997
Cited alongside, same era.
V. A. Yudin, “Lower bounds for spherical designs,” (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 61(3)
1997
P. Rungta, V. Buzek, C. M. Caves, M. Hillery, and G. J. Milburn, “Universal state inversion and concurrence in arbitrary dimensions,” Phys. Rev. A 64
2001
Later among the works it cites.
D. W. Leung, “Choi’s proof as a recipe for quantum process tomography,” J. Math. Phys. 44
2003
Later among the works it cites.
O. Christensen, An Introduction to Frames and Riesz Bases
2003
Later among the works it cites.
B. Collins, “Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral and free probability,” Int. Math. Res. Notes 17
2003
Later among the works it cites.
N. J. A. Sloane, R. H. Hardin and P. Cara, “Spherical designs in four dimensions,” in Proceedings of the 2003 IEEE Information Theory Workshop, La Sorbonne, Paris, France, 31 March - 4 April 2003, p. 253
2003
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
V. Bužek, R. Derka, G. Adam and P. L. Knight, “Reconstruction of quantum states of spin systems: from quantum Bayesian inference to quantum tomography,” Ann. Phys. 266
1998
Cited alongside, same era.
E. M. Rains, “Increasing subsequences and the classical groups,” Electron. J. Combin. 5
1998
Cited alongside, same era.
V. Levenshtein, “On designs in compact metric spaces and a universal bound on their size,” Discrete Math. 192
1998
Cited alongside, same era.
V. Levenshtein, “Universal bounds for codes and designs,” in V. Pless and C. W. Huffman (Eds.), Handbook of Coding Theory
1998
Cited alongside, same era.
K. Banaszek, G. M. D’Ariano, M. G. A. Paris and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61
1999
Cited alongside, same era.
C. M. Caves, “Quantum error correction and reversible operations,” J. Supercond. 12
1999
Cited alongside, same era.
M. Paris and J. Řeháček (Eds.), Quantum State Estimation
2004
Later among the works it cites.
J. M. Renes, R. Blume-Kohout, A. J. Scott and C. M. Caves, “Symmetric informationally complete quantum measurements,” J. Math. Phys. 45
2004
Later among the works it cites.
F. Tanaka and F. Komaki, “Bayesian predictive density operators for exchangeable quantum-statistical models,” Phys. Rev. A 71
2005
Later among the works it cites.
R. T. Horn, A. J. Scott, J. Walgate, R. Cleve, A. I. Lvovsky and B. C. Sanders, “Classical and quantum fingerprinting with shared randomness and one-sided error,” Quantum Inf. Comput. 5
2005
Later among the works it cites.
D. M. Appleby, “Symmetric informationally complete-positive operator valued measures and the extended Clifford group,” J. Math. Phys. 46
2005
Later among the works it cites.
H. F. Chau, “Unconditionally secure key distribution in higher dimensions by depolarization,” IEEE Trans. Inf. Theory 51
2005
Later among the works it cites.
E. Bannai, A. Munemasa and B. Venkov, “The nonexistence of certain tight spherical designs,” (Russian) Algebra i Analiz 16(4)
2005
Later among the works it cites.
A. J. Scott, “Tight informationally complete quantum measurements,” J. Phys. A 39
2006
Later among the works it cites.
B. Collins and P. Śniady, “Integration with respect to the Haar measure on unitary, orthogonal and symplectic group,” Comm. Math. Phys. 264
2006
Later among the works it cites.
S. T. Flammia, “On SIC-POVMs in prime dimensions,” J. Phys. A 39
2006
Later among the works it cites.
É. A. Shamsiev, “On calculation of integrals over spherical domains,” Ukrainian Math. J. 58
2006
Later among the works it cites.
D. Gross, K. Audenaert and J. Eisert, “Evenly distributed unitaries: on the structure of unitary designs,” J. Math. Phys. 48
2007
Closest in time.
A. Roy and A. J. Scott, “Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements,” J. Math. Phys. 48
2007
Closest in time.
P. de la Harpe, C. Pache and B. Venkov, “Construction of spherical cubature formulas using lattices,” (Russian) Algebra i Analiz 18(1)
2007
Closest in time.