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A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group.
Spherical codes and designs
P. Delsarte, J. M. Goethals, and J. J. Seidel · 1977
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On some spherical t-designs
E. Bannai · 1979
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2-transitive and antiflag transitive collineation groups of finite projective spaces
P. J. Cameron and W. M. Kantor · 1979
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Function Theory in the Unit Ball of ℂ n \mathbb{C}^{n}
W. Rudin · 1980
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Geometrical description of quantal state determination
I. D. Ivanović · 1981
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t t -designs in projective spaces
S. G. Hoggar · 1982
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Optimal state–determination by mutually unbiased measurements
W. K. Wootters and B. D. Fields · 1989
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On the eigenvalues of random matrices
M. S. Persi Diaconis · 1994
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Quantum Optics 2nd Edition
D. F. Walls and G. J. Milburn · 1994
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Permutation Groups
J. D. Dixon and B. Mortimer · 1996
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Non-binary unitary error bases and quantum codes
E. Knill · 1996
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Codes and Siegel modular forms
B. Runge · 1996
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Minimal characters of the finite classical groups
P. H. Tiep and A. E. Zalesskii · 1996
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Stabilizer Codes and Quantum Error Correction
D. Gottesman · 1997
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64 lines from a quaternionic polytope
S. G. Hoggar · 1998
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On designs in compact metric spaces and a universal bound on their size
V. Levenshtein · 1998
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Increasing subsequences and the classical groups
E. M. Rains · 1998
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Permutation Groups
P. J. Cameron · 1999
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Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
D. Gottesman and I. L. Chuang · 1999
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Spherical 7-designs in 2 n 2^{n} -dimensional Euclidean space
V. Sidelnikov · 1999
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Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2000
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The concentration of measure phenomenon
M. Ledoux · 2001
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The invariants of the Clifford groups
G. Nebe, E. M. Rains, and N. J. A. Sloane · 2001
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Entanglement measures under symmetry
K. G. H. Vollbrecht and R. F. Werner · 2001
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Antiflag-transitive collineation groups revisited
P. J. Cameron and W. M. Kantor · 2002
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Quantum data hiding
D. P. DiVincenzo, D. W. Leung, and B. M. Terhal · 2002
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Beyond stabilizer codes I: Nice error bases
A. Klappenecker and M. Rötteler · 2002
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Spherical designs and finite group representations (some results of E. Bannai)
P. de la Harpe and C. Pache · 2004
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Cross characteristic representations of even characteristic symplectic groups
R. Guralnick and P. Tiep · 2004
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Symmetric informationally complete quantum measurements
J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves · 2004
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Symmetric informationally complete-positive operator valued measures and the extended Clifford group
D. M. Appleby · 2005
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Universal quantum computation with ideal Clifford gates and noisy ancillas
S. Bravyi and A. Kitaev · 2005
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Unconditionally secure key distribution in higher dimensions by depolarization
H. F. Chau · 2005
Cited alongside, same era.
Efficient Simulation of Random Quantum States and Operators
C. Dankert · 2005
Cited alongside, same era.
Reexamination of optimal quantum state estimation of pure states
A. Hayashi, T. Hashimoto, and M. Horibe · 2005
Cited alongside, same era.
Mutually unbiased bases are complex projective 2-designs
A. Klappenecker and M. Rötteler · 2005
Cited alongside, same era.
Hudson’s Theorem for finite-dimensional quantum systems
D. Gross · 2006
Cited alongside, same era.
Quantum state tomography with fully symmetric measurements and product measurements
H. Zhu and B.-G. Englert · 2011
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The monomial representations of the Clifford group
D. M. Appleby, I. Bengtsson, S. Brierley, M. Grassl, D. Gross, and J.-Å. Larsson · 2012
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Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candès, T. Strohmer, and V. Voroninski · 2013
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Convergence of SDP hierarchies for polynomial optimization on the hypersphere, 2013
A. C. Doherty and S. Wehner · 2013
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Stabilizer information inequalities from phase space distributions
D. Gross and M. Walter · 2013
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Decoupling with unitary approximate two-designs
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Self-Dual Codes and Invariant Theory
G. Nebe, E. M. Rains, and N. J. A. Sloane · 2006
Cited alongside, same era.
Tight informationally complete quantum measurements
A. J. Scott · 2006
Cited alongside, same era.
Quantum t t -designs: t t -wise independence in the quantum world
A. Ambainis and J. Emerson · 2007
Cited alongside, same era.
Evenly distributed unitaries: On the structure of unitary designs
D. Gross, K. Audenaert, and J. Eisert · 2007
Cited alongside, same era.
Lie Groups: An Approach through Invariants and Representations
C. Procesi · 2007
Cited alongside, same era.
Quantum margulis expanders
D. Gross and J. Eisert · 2008
Cited alongside, same era.
O. Szehr, F. Dupuis, M. Tomamichel, and R. Renner · 2013
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States that look the same with respect to every basis in a mutually unbiased set
I. Amburg, R. Sharma, D. M. Sussman, and W. K. Wootters · 2014
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Solving quadratic equations via phaselift when there are about as many equations as unknowns
E. J. Candès and X. Li · 2014
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Complex spherical designs and codes
A. Roy and S. Suda · 2014
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Randomized benchmarking with confidence
J. J. Wallman and S. T. Flammia · 2014
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Quantum state estimation with informationally overcomplete measurements
H. Zhu · 2014
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Galois unitaries, mutually unbiased bases, and MUB-balanced states
D. M. Appleby, I. Bengtsson, and H. B. Dang · 2015
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Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem
D. M. Appleby, C. A. Fuchs, and H. Zhu · 2015
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Local random quantum circuits are approximate polynomial-designs, 2015
F. G. S. L. Brandao, A. W. Harrow, and M. Horodecki · 2015
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Phase retrieval from coded diffraction patterns
E. J. Candès, X. Li, and M. Soltanolkotabi · 2015
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Near-linear constructions of exact unitary 2-designs, Apr. 2015
R. Cleve, D. Leung, L. Liu, and C. Wang · 2015
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Entropic uncertainty relations and their applications
P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner · 2015
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A partial derandomization of PhaseLift using spherical designs
D. Gross, F. Krahmer, and R. Kueng · 2015
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Stable low-rank matrix recovery via null space properties, 2015
M. Kabanava, R. Kueng, H. Rauhut, and U. Terstiege · 2015
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Quantum Compressed Sensing Using 2-Designs, Oct. 2015
S. Kimmel and Y.-K. Liu · 2015
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Qubit stabilizer states are complex projective 3-designs, 2015
R. Kueng and D. Gross · 2015
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The Clifford group forms a unitary 3-design, 2015
Z. Webb · 2015
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Multiqubit Clifford groups are unitary 3-designs, 2015
H. Zhu · 2015
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Sharply covariant mutually unbiased bases, 2015
H. Zhu · 2015
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Super-symmetric informationally complete measurements
H. Zhu · 2015
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Representations of the multi-qubit Clifford group
J. Helsen, J. Wallman, and S. Wehner · 2016
Closest in time.
Distinguishability of quantum states under Clifford orbits, 2016
R. Kueng, H. Zhu, and D. Gross · 2016
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Low rank matrix recovery from Clifford orbits, 2016
R. Kueng, H. Zhu, and D. Gross · 2016
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Multipartite Entanglement in Stabilizer Tensor Networks, Aug. 2016
S. Nezami and M. Walter · 2016
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Permutation symmetry determines the discrete wigner function
H. Zhu · 2016
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