References
- William K Wootters and Brian D Fields (1989). Optimal state-determination by mutually unbiased measurements. Annals of Physics, 191(2): 363–381.
- Philippe Raynal, Xin Lü and Berthold-Georg Englert (2011). Mutually unbiased bases in six dimensions: The four most distant bases. Phys. Rev. A, 83: 062303.
- Daniel McNulty and Stefan Weigert (2012). The limited role of mutually unbiased product bases in dimension 6. Journal of Physics A: Mathematical and Theoretical, 45(10): 102001.
- Lin Chen and Li Yu (2018). Mutually unbiased bases in dimension six containing a product-vector basis. Quantum Information Processing, 17(8): 198.
- Daniel McNulty and Stefan Weigert (2012). All mutually unbiased product bases in dimension 6. Journal of Physics A: Mathematical and Theoretical, 45(13): 135307.
- Daniel McNulty, Bogdan Pammer and Stefan Weigert (2016). Mutually unbiased product bases for multiple qudits. Journal of Mathematical Physics, 57(3).
- DANIEL MCNULTY and STEFAN WEIGERT (2012). On the impossibility to extend triples of mutually unbiased product bases in dimension six. International Journal of Quantum Information, 10(05): 1250056.
- Lin Chen and Li Yu (2017). Product states and Schmidt rank of mutually unbiased bases in dimension six. Journal of Physics A Mathematical General, 50(47): 475304.
- P. O. Boykin, M. Sitharam, P. H. Tiep and P. Wocjan (2005). Mutually Unbiased Bases and Orthogonal Decompositions of Lie Algebras.
- Stephen Brierley and Stefan Weigert (2008). Maximal sets of mutually unbiased quantum states in dimension 6. Phys. Rev. A, 78: 042312.
- Stephen Brierley and Stefan Weigert (2010). Mutually Unbiased Bases and Semi-definite Programming. Journal of Physics: Conference Series, 254: 012008.
- Sébastien Designolle, Paul Skrzypczyk, Florian Fröwis and Nicolas Brunner (2018). Quantifying measurement incompatibility of mutually unbiased bases.
- M. Wiesniak, T. Paterek and A. Zeilinger (2011). Entanglement in mutually unbiased bases. New Journal of Physics, 13(5): 053047.
- T. Durt, B.-G. Englert, I. Bengtsson and K. Zyczkowski (2010). On mutually unbiased bases. Int. J. Quantum Information, 8(4): 535–640.
- Bengt R. Karlsson (2011). Three-parameter complex Hadamard matrices of order 6. Linear Algebra and its Applications,434(1): 247–258.
- U. Haagerup (1997). Orthogonal maximal abelian *-subalgebras of the n × n matrices and cyclic n-roots. International Press.
- Terence Tao (2004). Fuglede’s conjecture is false in 5 and higher dimensions. Math. Res. Lett., 11: 251.
- Ferenc Szöllösi (2012). Complex Hadamard matrices of order 6: a four-parameter family. Journal of the London Mathematical Society, 85(3): 616–632.
- Mengfan Liang and Lin Chen (2024). Eigenvalues and eigenvectors of complex hadamard matrices.
- Beauchamp Kyle and Nicoara Remus (2006). Orthogonal maximal abelian *-subalgebras of the 6 × 6 matrices. Linear Algebra and Its Applications, 428(8): 1833–1853.
- Tadej, Wojciech and K.Zyczkowski (2006). A concise guide to complex Hadamard matrices. Open Systems and Information Dynamics, 13(2): 133–177.
- T. Banica, J. Bichon and J.M. Schlenker (2009). Representations of quantum permutation algebras. Journal of Functional Analysis, 257(9): 2864–2910.
- W.D. Launey and D.M. Gordon (2001). A comment on the Hadamard conjecture. Journal of Combinatorial Theory, Series A, 95(1): 180–184.
- P. Dita (2002). New results on the parametrisation of complex Hadamard matrices. Journal of Physics A General Physics, 37(20): 5355.
- G. Hiranandani and J.M. Schlenker (2014). Small circulant complex Hadamard matrices of Butson type. European Journal of Combinatorics, 51: 306–314.
- Harold Ollivier and Wojciech H. Zurek (2001). Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett., 88: 017901, Dec.
- J. I. Cirac and P. Zoller (1995). Quantum computations with cold trapped ions. Phys. Rev. Lett., 74: 4091–4094, May.
- Lin Chen and Li Yu (2014). Nonlocal and controlled unitary operators of Schmidt rank three. Phys. Rev. A, 89: 062326.
- Lin Chen and Li Yu (2014). On the Schmidt-rank-three bipartite and multipartite unitary operator. Annals of Physics, 351: 682–703.
- P. Dita (2004). Some results on the parametrization of complex hadamard matrices. Journal of Physics A: Mathematical and General, 37(20): 5355.
- Terence Tao (2004). Fuglede’s conjecture is false in 5 and higher dimensions. Mathematical Research Letters, 11(2): 251–258.
- A. T. Butson (1962). Generalized hadamard matrices. Proceedings of the American Mathematical Society, 13: 894–898.
- Kyle Beauchamp and Remus Nicoara (2008). Orthogonal maximal abelian *-subalgebras of the 6 × 6 matrices. Linear Algebra and its Applications, 428(8): 1833–1853.
- Lin Chen and Li Yu (2015). Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates. Phys. Rev. A, 91: 032308.
Language: English
Page range: 192 - 209
Submitted on: Jan 14, 2026
Accepted on: Mar 3, 2026
Published on: Jun 4, 2026
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
© 2026 Yanzu Huang, Lin Chen, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.