Fetching the paper…
Reading the bibliography…
The existence of $k$-uniform states has been a widely studied problem due to their applications in several quantum information tasks and their close relation to combinatorial objects like Latin squares and orthogonal arrays.
H. Robbins, “A remark on Stirling’s formula,” The American Mathematical Monthly , vol. 62, no. 1, pp. 26–29, 1955
1955
Earlier work this paper cites.
F. MacWilliams, C. Mallows, and N. Sloane, “Generalizations of Gleason’s theorem on weight enumerators of self-dual codes,” IEEE Transactions on Information Theory , vol. 18, no. 6, pp. 794–805, 1972
1972
Earlier work this paper cites.
C. L. Mallows and N. J. A. Sloane, “An upper bound for self-dual codes,” Information and Control , vol. 22, no. 2, pp. 188–200, 1973
1973
Earlier work this paper cites.
P. Shor and R. Laflamme, “Quantum analog of the MacWilliams identities for classical coding theory,” Physical Review Letters , vol. 78, no. 8, pp. 1600–1602, 1997
1997
Earlier work this paper cites.
D. Bertsimas and J. N. Tsitsiklis, Introduction to linear optimization . Athena Scientific, 1997
1997
Earlier work this paper cites.
E. M. Rains, “Shadow bounds for self-dual codes,” IEEE Transactions on Information Theory , vol. 44, no. 1, pp. 134–139, 1998
1998
Earlier work this paper cites.
E. M. Rains, “Quantum weight enumerators,” IEEE Transactions on Information Theory , vol. 44, no. 4, pp. 1388–1394, 1998
1998
Earlier work this paper cites.
A. R. Calderbank, E. M. Rains, P. M. Shor, and N. J. A. Sloane, “Quantum error correction via codes over GF(4),” IEEE Transactions on Information Theory , vol. 44, no. 4, pp. 1369–1387, 1998
1998
Earlier work this paper cites.
A. Ashikhmin and S. Litsyu, “Upper bounds on the size of quantum codes,” IEEE Transactions on Information Theory , vol. 45, no. 4, pp. 1206–1215, 1999
1999
Earlier work this paper cites.
E. M. Rains, “Quantum shadow enumerators,” IEEE Transactions on Information Theory , vol. 45, no. 7, pp. 2361–2366, 1999
1999
Earlier work this paper cites.
A. J. Scott, “Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions,” Physical Review A , vol. 69, no. 5, p. 052330, 2004
2004
Cited alongside, same era.
S. Han and J. K. Lee, “Nonexistence of some extremal self-dual codes,” Journal of the Korean Mathematical Society , vol. 43, no. 6, pp. 1357–1369, 2006
2006
Cited alongside, same era.
R. A. Bertlmann and P. Krammer, “Bloch vectors for qudits,” Journal of Physics A: Mathematical and Theoretical , vol. 41, no. 23, p. 235303, 2008
2008
Cited alongside, same era.
S. Han and J. L. Kim, “The nonexistence of near-extremal formally self-dual codes,” Designs Codes and Cryptography , vol. 51, no. 1, pp. 69–77, 2009
2009
Cited alongside, same era.
W. Helwig, W. Cui, J. I. Latorre, A. Riera, and H. K. Lo, “Absolute maximal entanglement and quantum secret sharing,” Physical Review A , vol. 86, no. 5, p. 052335, 2012
M. Li and Y. Wang, “ k k -uniform quantum states arising from orthogonal arrays,” Physical Review A , vol. 99, no. 4, p. 042332, 2019
2019
Later among the works it cites.
Z. Raissi, A. Teixidó, C. Gogolin, and A. Acín, “Constructions of k k -uniform and absolutely maximally entangled states beyond maximum distance codes,” Physical Review Research , vol. 2, no. 3, p. 033411, 2020
2020
Later among the works it cites.
F. Huber and M. Grassl, “Quantum codes of maximal distance and highly entangled subspaces,” Quantum , vol. 4, p. 284, 2020
2020
Later among the works it cites.
F. Shi, M. Li, L. Chen, and X. Zhang, “ k k -uniform quantum information masking,” Physical Review A , vol. 104, no. 3, p. 032601, 2021
2021
Later among the works it cites.
F. Shi, Y. Shen, L. Chen, and X. Zhang, “ k k -uniform states in heterogeneous systems,” IEEE Transactions on Information Theory , vol. 68, no. 5, pp. 3115–3129, 2022
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2012
Cited alongside, same era.
D. Goyeneche and K. Życzkowski, “Genuinely multipartite entangled states and orthogonal arrays,” Physical Review A , vol. 90, no. 2, p. 022316, 2014
2014
Cited alongside, same era.
D. Goyeneche, D. Alsina, J. I. Latorre, A. Riera, and K. Życzkowski, “Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices,” Physical Review A , vol. 92, no. 3, p. 032316, 2015
2015
Cited alongside, same era.
K. Feng, L. Jin, C. Xing, and C. Yuan, “Multipartite entangled states, symmetric matrices, and error-correcting codes,” IEEE Transactions on Information Theory , vol. 63, no. 9, pp. 5618–5627, 2017
2017
Cited alongside, same era.
F. Huber, O. Gühne, and J. Siewert, “Absolutely maximally entangled states of seven qubits do not exist,” Physical Review Letters , vol. 118, no. 20, p. 200502, 2017
2017
Cited alongside, same era.
F. Huber, C. Eltschka, J. Siewert, and O. Gühne, “Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity,” Journal of Physics A: Mathematical and Theoretical , vol. 51, no. 17, p. 175301, 2018
2018
Cited alongside, same era.
2022
Later among the works it cites.
M. Grassl, F. Huber, and A. Winter, “Entropic proofs of singleton bounds for quantum error-correcting codes,” IEEE Transactions on Information Theory , vol. 68, no. 6, pp. 3942–3950, 2022
2022
Later among the works it cites.
F. Huber and N. Wyderka, “Table of AME states,” Online available at https://tp.nt.uni-siegen.de/ame/ame.html , accessed on 2024-12-09
2024
Later among the works it cites.
M. Grassl, “Bounds on the minimum distance of linear codes and quantum codes,” Online available at http://www.codetables.de , 2007, accessed on 2024-12-09
2024
Later among the works it cites.
F. Shi, Y. Ning, Q. Zhao, and X. Zhang, “Bounds on k k -uniform quantum states,” IEEE Transactions on Information Theory , vol. 71, no. 1, pp. 413–425, 2025
2025
Closest in time.